1. A photonic quantum information processing apparatus (100) for processing multipartite entangled states under programmable noisy quantum-channel conditions, comprising: an entangled-photon source unit (102) configured to generate an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state, the entangled-photon source unit (102) comprising: a coherent pump laser (114); at least one nonlinear optical element (116) configured for at least one of spontaneous parametric down-conversion and an equivalent probabilistic entangled-photon generation process; one or more interferometric arrangements comprising polarization-manipulation optics (118) configured to generate polarization-entangled photon pairs with a controllable balance between logical basis components; and at least one of a cascaded nonlinear processing subunit (120A) and a parallel nonlinear processing subunit (120B) configured to generate at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to noisy quantum channels; a plurality of programmable amplitude-damping channel (ADC) emulators (106) optically coupled to receive each respective qubit of the GHZ-type entangled state from the entangled-photon source unit (102), each ADC emulator comprising a polarization-dependent interferometric circuit (124) with at least one variable polarization-rotation element (126) and beam-splitting element (128), configured to: direct different polarization components of an input photon into distinct optical paths; apply a controllable polarization rotation in each of the distinct optical paths; and at least one of recombine and route resulting components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit; a plurality of local Pauli-X control units (104) arranged in the optical paths between the entangled-photon source unit (102) and the plurality of ADC emulators (106), comprising independently addressable polarization-rotation elements (126) positioned upstream of the amplitude-damping channel emulators, configured to selectively implement at least one of an identity operation, a Pauli-X operation on individual photons before amplitude-damping evolution, causing subset of qubits to flip corresponding to a programmable control pattern; a polarization-analysis and detection subsystem (108) optically coupled to receive photons emerging from the plurality of ADC emulators (106), comprising: polarization-manipulation optics (130) configured to realize projective measurements in multiple polarization bases; one or more beam-splitting elements (132) for basis discrimination; an array of single-photon detectors (134); and coincidence-counting subunit (136) comprising at least one time-tagging unit configured to register multi-fold coincidence events; a controlled quantum teleportation unit (110) optically coupled to receive photons emerging from the plurality of ADC emulators (106), configured to use the n-qubit GHZ-type entangled states as controlled quantum teleportation channels, the controlled quantum teleportation unit (110) comprising: a sender unit (138) comprising a source of single photons with polarization encoded input state to teleport and a measurement stage to perform a Bell-type joint measurement between the input state and a channel photon with a detection assembly outputting at least two classical bits; at least one controller unit (140) receiving a channel photon, comprises polarization-rotation optics with at least two selectable settings corresponding to an allow-teleportation condition and an abort-teleportation condition, along with a detection assembly outputting at least one classical control bit; and a receiver unit (142) to receive a channel photon, comprises polarization-analysis optics to implement Pauli corrections on the photon based on classical information received from the sender unit (138) and controller unit (140) and to measure a teleported output state; a processor (112) operatively coupled to the entangled-photon source unit (102), the plurality of ADC emulators (106), the local Pauli-X control unit (104), the polarization-analysis and detection subsystem (108), and the controlled quantum teleportation unit (110), wherein the processor (112) is configured to: set, for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators (106) select based on a GHZ-symmetric parametrization of the output multipartite state and a target performance criterion; apply periodically, selective Pauli-X operations to a selected subset of qubits by controlling the local Pauli-X control unit (104); reconstruct, from coincidence-count data, a density matrix of an output multipartite quantum state via quantum state tomography; compute multipartite entanglement metrics for the reconstructed state and, for at least three-qubit states, to classify the state into entanglement classes using a GHZ symmetric parametrization; and compute controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers, and correlate the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.

2. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the entangled‑photon source unit (102) comprises: one or more bidirectionally interferometer comprising a sagnac-type interferometer and one or more periodically poled potassium titanyl phosphate crystal configured to generate polarization entangled photon pairs; and optionally a second non-linear stage pumped by one photon of the polarized-entangled pairs to generate at least one of the three-photon GHZ-type entangled state and the four-photon GHZ-type entangled state.

3. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein each amplitude‑damping channel emulator comprises: a displaced Sagnac interferometer configured to manage a horizontal polarization input in a first spatial mode and to convert a vertical polarization input into a mixture of a vertical component remaining in the first spatial mode and a horizontal component diverted to a second spatial mode, with the relative weight between the components controlled by the angle of the variable polarization‑rotation element (126) to realize a damping probability of the sine squared of twice an angle.

4. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein each independently addressable polarization‑rotation element (122) of the local Pauli‑X control unit (104) comprises: a local polarization rotator configured to implement an identity operation and a Pauli‑X operation on the polarization of the corresponding photon.

5. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the polarization‑manipulation optics (130) of the polarization‑analysis and detection subsystem (108) comprise: polarization analyzers configured to realize projective measurements in at least one of a horizontal-vertical polarization basis, a diagonal-anti-diagonal polarization basis, and a right-circular-left-circular polarization basis.

6. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the sender unit (138) of the controlled quantum teleportation unit (110) comprises: a source of polarization-correlated photon pairs, preparation stage configured to prepare an arbitrary polarization state to be teleported, a controller unit to allow or abort teleportation and measurement stage to perform a partial Bell-state measurement between the prepared state and a channel photon from the amplitude-damping channel emulator.

7. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the at least one controller unit (140) of the controlled quantum teleportation unit (110) comprises polarization-rotation optics to a first angle: a quarter‑wave plate settable to a first angle corresponding to an abort‑teleportation condition and a second angle corresponding to an allow‑teleportation condition, followed by a polarizing beam splitter and a plurality of single‑photon detectors.

8. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the receiver unit (142) of the controlled quantum teleportation unit (110) comprises: polarization-analysis optics configured to implement at least one of a identity correction, a Pauli‑X correction, a Pauli‑Z correction, and a Pauli‑Y correction on the received channel photon based on classical bits received from the sender unit (138) and the controller unit (140).

9. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the processor (112) is further configured to: store reference trajectories of multipartite entanglement metrics and controlled quantum teleportation fidelity as functions of at least one of an amplitude‑damping strength, an initial GHZ-type amplitude, and a Pauli‑X control pattern; and compare measured trajectories onto the reference trajectories in a graphical user interface to validate amplitude‑damping emulation and guide selection of Pauli‑X schedules.

10. A method (1200) for processing multipartite entangled states under programmable noisy quantum-channel conditions, the method (1200) comprising: generating, by a photonic quantum information processing apparatus (100), an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state via an entangled-photon source unit (102); directing, by the apparatus (100), photons representing each respective qubit of the GHZ-type entangled state emerging from the entangled-photon source unit (102) into a corresponding one of a plurality of programmable amplitude-damping channel (ADC) emulators (106); directing, by the apparatus (100), in each ADC emulator, different polarization components of the input photon from the entangled-photon source unit (102) into distinct optical paths; applying, by the apparatus (100), in each distinct optical path of the ADC emulator (106), a controllable polarization rotation to the polarization components; routing, by the apparatus (100), from each ADC emulator, resulting polarization components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit; arranging, by the apparatus (100), a local Pauli-X control unit (104) in the optical paths between the entangled-photon source unit (102) and the plurality of ADC emulators (106), and selectively implementing, using independently addressable polarization-rotation elements (126) positioned upstream of the amplitude-damping channel emulators, at least one of an identity operation, a Pauli-X operation on individual photons of the GHZ-type entangled state before the photons enter the amplitude-damping channel emulators, causing a subset of qubits to flip according to a programmable control pattern; directing, by the apparatus (100), photons emerging from the plurality of ADC emulators (106) to a polarization-analysis and detection subsystem, and, in the polarization-analysis and detection subsystem (108); directing, by the apparatus (100), a first portion of the photons emerging from the plurality of ADC emulators (106) to the polarization-analysis and detection subsystem and directing a second portion of the photons emerging from the plurality of ADC emulators (106) to a controlled quantum teleportation unit (110), both subsystems being optically coupled to receive photons from the ADC emulators (106); setting, by the apparatus (100), for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators (106) using a processor operatively coupled to the entangled-photon source unit (102), the plurality of ADC emulators, the local Pauli-X control unit (104), the polarization-analysis and detection subsystem (108), and the controlled quantum teleportation unit (110); applying periodically, by the apparatus (100), via the processor (112) and the local Pauli-X control unit (104), selective Pauli-X operations to a selected subset of qubits of the GHZ-type entangled state propagating between the entangled-photon source unit (102) and the plurality of ADC emulators (106); reconstructing, by the apparatus (100), via the processor (112), from coincidence-count data generated by the polarization-analysis and detection subsystem (108), a density matrix of an output multipartite quantum state via quantum state tomography; computing, by the apparatus (100), via the processor (112), multipartite entanglement metrics for the reconstructed density matrix and, for at least three-qubit states, classifying the state into entanglement classes using a GHZ symmetric parametrization; and computing, by the apparatus (100), via the processor (112), controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers from data generated by the controlled quantum teleportation unit (110), and correlating the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.

11. The method (1200) as claimed in claim 10, wherein generating the n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state comprises: pumping, by the apparatus (100), at least one nonlinear optical element (116) with a coherent pump laser (114) for at least one of spontaneous parametric down-conversion and an equivalent probabilistic entangled-photon generation process; generating, by the apparatus (100), polarization-entangled photon pairs with a controllable balance between logical basis components using one or more interferometric arrangements comprising polarization-manipulation optics (118); and generating, by the apparatus (100), at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to quantum communication channels using at least one of a cascaded nonlinear processing subunit (120A) and a parallel nonlinear processing subunit (120B).

12. The method (1200) as claimed in claim 10, further comprising optically coupling, by the apparatus (100), the plurality of programmable amplitude-damping channel (ADC) emulators (106) to receive each respective qubit of the GHZ-type entangled state directly from the entangled-photon source unit (102).

13. The method (1200) as claimed in claim 10, further comprising: positioning independently, by the apparatus (100), addressable polarization-rotation elements (122) of the local Pauli-X control unit (104) upstream of the amplitude-damping channel emulators.

14. The method (1200) as claimed in claim 10, wherein directing photons emerging from the plurality of ADC emulators (106) to the polarization-analysis and detection subsystem (108) comprises: realizing, by the apparatus (100), projective measurements in multiple polarization bases using polarization-manipulation optics (130); discriminating, by the apparatus (100), measurement bases using one or more beam-splitting elements (132); detecting, by the apparatus (100), photons with an array of single-photon detectors (134); and recording, by the apparatus (100), multi-fold coincidence events with a coincidence-counting subunit (136) comprising at least one time-tagging unit.

15. The method (1200) as claimed in claim 1, wherein directing photons emerging from the plurality of ADC emulators (106) to the controlled quantum teleportation unit (110) comprises: providing, by the apparatus (100), in a sender unit (138), a source of single photons with polarization encoding an input state to teleport and performing a Bell-type joint measurement between the input state and a channel photon; setting, by the apparatus (100), in at least one controller unit (140) receiving a channel photon, polarization-rotation optics to at least one of an allow-teleportation condition and an abort-teleportation condition, detecting the controller photon, and outputting at least one classical control bit; and implementing, by the apparatus (100), in a receiver unit (142) receiving a channel photon, Pauli corrections on the photon based on classical information received from the sender unit (142) and controller unit (140) and measuring a teleported output state.

16. The method (1200) as claimed in claim 10, wherein generating the GHZ-type entangled state comprises: operating, by the apparatus (100) via the entangled-photon source unit (102), a first Sagnac interferometer comprising a periodically poled potassium titanyl phosphate crystal pumped bidirectionally by the coherent pump laser (114) to generate polarization-entangled photon pairs; and operating, by the apparatus (100), a second Sagnac interferometer comprising a periodically poled lithium niobate waveguide crystal pumped by one photon of the polarization-entangled photon pairs to generate additional photons, to generate at least one of the three-photon GHZ-type entangled state and the four-photon GHZ-type entangled state.

Description:PREAMBLE TO THE DESCRIPTION
The following specification particularly describes the invention and the manner in which it is to be performed.
 
TECHNICAL FIELD
Embodiments of the present disclosure generally relate to photonic quantum communication systems and more particularly relate to a photonic quantum information processing apparatus and method for processing multipartite entangled-states under noisy quantum-channel conditions.
BACKGROUND
Generally, photonic network architectures leverage entanglement as a key resource for quantum computation, communication, and sensing. Entangled photon states serve as carriers of quantum information across multi-node networks, supporting tasks such as quantum teleportation, distributed sensing, and secure communication protocols. The ability to generate, manipulate, and preserve multipartite entangled states in photonic platforms is critical for the development of scalable quantum technologies. The entanglement is a crucial resource in quantum information applications, yet real qubit platforms, such as neutral atoms and superconducting transmons, suffer from amplitude-damping noise or energy relaxation, leading to entanglement decay. In contrast, free-space or integrated photonic qubits, including polarization- and path-encoded qubits, exhibit negligible amplitude decay under normal conditions. Existing systems lack a physical photonic platform that allows controlled simulation of amplitude-damping dynamics, exploration of entanglement-preserving strategies, and application to multi-qubit quantum teleportation while mapping resulting entangled states to corresponding entanglement Stochastic Local Operations and Classical Communication (SLOCC) classes.
Additionally, conventional photonic circuits and experimental setups provide tools for entangled-state generation, Bell-state measurements, or individual amplitude-damping event heralding. However, none of these approaches integrates programmable amplitude-damping channels with local Pauli-X operations for preserving entanglement, nor do they map multipartite entanglement into classes such as GHZ, W, biseparable, or separable for n-qubit systems. Similarly, prior photonic teleportation systems lack provisions for simultaneous diagnostics of entanglement and teleportation fidelity under controlled noise conditions. Subsequently, the ability to selectively apply NOT operations to qubits enables task-dependent preservation strategies. Flipping a single qubit may optimally preserve genuine multipartite concurrence, while flipping all qubits may better preserve controlled quantum teleportation fidelity. Moreover, mixed biseparable GHZ-type states can maintain non-classical teleportation fidelity even after global entanglement metrics decay to zero. Conventional systems do not provide the experimental capability to explore these distinctions in real time across multiple qubits under identical but independent amplitude-damping noise.
In existing photonic and matter-qubit platforms, components such as amplitude-damping heralding circuits, entangled-state sources, and Bell analyzers are available. Nonetheless, a compact optical circuit capable of simulating neutral-atom-like amplitude-damping noise on three- and four-qubit entangled photonic states, applying local Pauli-X unitary operations for entanglement preservation, and integrating controlled quantum teleportation with entanglement classification remains unavailable. Such a system would provide unprecedented insights into the integrity of quantum information and the effectiveness of noise-mitigation strategies.
Consequently, there is a need in the art for a photonic quantum information processing apparatus and method for processing multipartite entangled-states under quantum-channel conditions, to address at least the aforementioned issues in the prior arts.
SUMMARY
This summary is provided to introduce a selection of concepts, in a simple manner, which is further described in the detailed description of the disclosure. This summary is neither intended to identify key or essential inventive concepts of the subject matter nor to determine the scope of the disclosure.
An aspect of the present disclosure provides a photonic quantum information processing apparatus for processing multipartite entangled states under programmable noisy quantum-channel conditions. Further, the apparatus may include an entangled-photon source unit configured to generate an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state. Further, the entangled source unit may include a coherent pump laser, at least one nonlinear optical element configured for at least one of spontaneous parametric down conversion and an equivalent probabilistic entangled photon generation process. Further, the entangled-photon source unit includes one or more interferometric arrangements comprising polarization-manipulation optics configured to generate polarization-entangled photon pairs with a controllable balance between logical basis components. Furthermore, the entangled-photon source unit includes at least one of a cascaded nonlinear processing subunit and a parallel nonlinear processing subunit configured to generate at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to noisy quantum channels. Further, the photonic quantum information processing apparatus includes a plurality of programmable amplitude-damping channel (ADC) emulators optically coupled to receive each respective qubit of the GHZ-type entangled state from the entangled photon source unit. Further, each ADC emulator may include a polarization dependent interferometric circuit with at least one variable polarization-rotation element and beam-splitting element. Further, each ADC emulator may be configured to direct different polarization components of an input photon into distinct optical paths, apply a controllable polarization rotation in each of the distinct optical paths. Further, each ADC emulator may be configured to at least one of recombine and route resulting components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit. Further, the apparatus may include a local Pauli X control unit arranged in the optical paths between the entangled-photon source unit and the plurality of ADC emulators.
Further, the local Pauli X control unit may include independently addressable polarization-rotation elements positioned upstream of the amplitude-damping channel emulators, configured to selectively implement at least one of an identity operation, a Pauli X operation and a NOT operation on individual photons before amplitude-damping evolution, causing subset of qubits to flip corresponding to a programmable control pattern. Further, the apparatus may include a polarization-analysis and detection subsystem optically coupled to receive photons emerging from the plurality of ADC emulators. Further, the polarization-analysis and detection subsystem may include polarization-manipulation optics configured to realize projective measurements in multiple polarization bases. Further, the polarization-analysis and detection subsystem may include one or more beam-splitting elements for basis discrimination, an array of single-photon detectors, and coincidence-counting subunit including at least one time-tagging unit configured to register multi-fold coincidence events, coincidence-counting subunit may include at least one time-tagging unit configured to register multi-fold coincidence events. Further, the apparatus may include a controlled quantum teleportation unit optically coupled to receive photons emerging from the plurality of ADC emulators. Further, the controlled quantum teleportation unit may be configured to use the GHZ-type entangled states as controlled quantum teleportation channels. \The controlled quantum teleportation unit includes, a sender unit including a source of single photons with polarization encoding an input state to teleport and a measurement stage to perform a Bell-type joint measurement between the input state and a channel photon with a detection assembly outputting at least two classical bits. Further, controlled quantum teleportation unit includes at least one controller unit receiving a channel photon, comprises polarization-rotation optics with at least two selectable settings corresponding to an allow-teleportation condition and an abort-teleportation condition, along with a detection assembly outputting at least one classical control bit. Further, the controlled quantum teleportation unit includes a receiver unit to receive a channel photon, comprises polarization-analysis optics to implement Pauli corrections on the photon based on classical information received from the sender and controller modules and to measure a teleported output state.
Further, the apparatus may include a processor operatively coupled to the entangled-photon source unit, the plurality of ADC emulators, the local Pauli-X control unit, the polarization-analysis and detection subsystem, and the controlled quantum teleportation unit. Further, the processor may be configured to, set, for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators. Furthermore, the processor may be configured to apply periodically, selective Pauli-X operations to a selected subset of qubits by controlling the local Pauli-X control unit, reconstruct, from coincidence-count data, a density matrix of an output multipartite quantum state via quantum state tomography. Further, the processor may be configured to compute multipartite entanglement metrics for the reconstructed state and, for at least three-qubit states, to classify the state into entanglement classes comprising at least one of a Greenberger-Horne-Zeilinger (GHZ) class, a W class, biseparable class, and a separable class using a GHZ symmetric parametrization. Furthermore, the processor may be configured to compute controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers, and correlate the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.
Another aspect of the present disclosure provides a method for processing multipartite entangled-states under programmable noisy quantum-channel conditions. The method may include generating an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state via an entangled photon source unit. Further, the method may include directing photons representing each respective qubit of the GHZ-type entangled state emerging from the entangled-photon source unit into a corresponding one of a plurality of programmable amplitude-damping channel (ADC) emulators. Further, the method may include directing in each ADC emulator, different polarization components of the input photon from the entangled-photon source unit into distinct optical paths. Further, the method may include applying, in each distinct optical path of the ADC emulator, a controllable polarization rotation to the polarization components. Further, the method may include routing, from each ADC emulator, resulting polarization components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit. Further, the method may include arranging a local Pauli-X control unit in the optical paths between the entangled-photon source unit and the plurality of ADC emulators. Further, the method may include selectively implementing, using independently addressable polarization-rotation elements positioned upstream of the amplitude-damping channel emulators, at least one of an identity operation, a Pauli-X operation on individual photons of the GHZ-type entangled state before the photons enter the amplitude-damping channel emulators, causing a subset of qubits to flip according to a programmable control pattern.
Further, the method may include directing photons emerging from the plurality of ADC emulators to a polarization-analysis and detection subsystem, and, in the polarization-analysis and detection subsystem. Further, the method may include directing a first portion of the photons emerging from the plurality of ADC emulators to the polarization-analysis and detection subsystem and directing a second portion of the photons emerging from the plurality of ADC emulators to a controlled quantum teleportation unit, both subsystems being optically coupled to receive photons from the ADC emulators. Further, the method may include setting for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators using a processor operatively coupled to the entangled-photon source unit, the plurality of ADC emulators, the local Pauli-X control unit, the polarization-analysis and detection subsystem, and the controlled quantum teleportation unit. Further, the method may include applying periodically via the processor and the local Pauli-X control unit, selective Pauli-X operations to a selected subset of qubits of the GHZ-type entangled state propagating between the entangled-photon source unit and the plurality of ADC emulators. Further, the method may include reconstructing via the processor, from coincidence-count data generated by the polarization-analysis and detection subsystem, a density matrix of an output multipartite quantum state via quantum state tomography. Further, the method may include computing, via the processor, multipartite entanglement metrics for the reconstructed density matrix and, for at least three-qubit states, classifying the state into entanglement classes comprising at least one of a Greenberger-Horne–Zeilinger (GHZ) class, a W class, biseparable class, and a separable class using a GHZ symmetric parametrization. Further, the method may include computing, via the processor, controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers from data generated by the controlled quantum teleportation unit, and correlating the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.
To further clarify the advantages and features of the present disclosure, a more particular description of the disclosure will follow by reference to specific embodiments thereof, which are illustrated in the appended figures. It is to be appreciated that these figures depict only typical embodiments of the disclosure and are therefore not to be considered limiting in scope. The disclosure will be described and explained with additional specificity and detail with the appended figures.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles. In the figures, the left-most digit(s) of a reference number identify the figure in which the reference number first appears. The same numbers are used throughout the figures to reference features and components. Some embodiments of system and/or methods in accordance with embodiments of the present subject matter are now described, by way of example only, and with reference to the accompanying figures, in which:
FIG. 1 illustrates an exemplary block diagram representation of a photonic quantum information processing apparatus, in accordance with an embodiment of the present disclosure;
FIG. 2 illustrates an exemplary block diagram representation of a photonic quantum information processing apparatus for a three-qubit GHZ setup, in accordance with an embodiment of the present disclosure;
FIG. 3 illustrates an exemplary schematic diagram representation for preparation of a three-qubit GHZ setup of a photonic quantum information processing apparatus, in accordance with an embodiment of the present disclosure;
FIG. 4 illustrates an exemplary schematic framework representation for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a three-qubit GHZ state, in accordance with an embodiment of the present disclosure;
FIG. 5 illustrates an exemplary block diagram representation of a photonic quantum information processing apparatus for a four-qubit GHZ setup, in accordance with an embodiment of the present disclosure;
FIG. 6 illustrates an exemplary schematic diagram representation for preparation of a four-qubit GHZ setup of a photonic quantum information processing apparatus, in accordance with an embodiment of the present disclosure;
FIG. 7 illustrates an exemplary schematic framework representation for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a four-qubit GHZ state, in accordance with an embodiment of the present disclosure;
FIG. 8A illustrates an exemplary graphical representation, depicting an evolution of entanglement of three-photon GHZ state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure;
FIG. 8B illustrates an exemplary graphical representation, depicting an entanglement decay with respect to damping probability of a three-photon GHZ state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure;
FIG. 9A illustrates an exemplary graphical representation, depicting an evolution of entanglement of four-photon GHZ state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure;
FIG. 9B illustrates an exemplary graphical representation, depicting an entanglement decay with respect to damping probability of a four-photon GHZ state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure;
FIG. 10 illustrates an exemplary graphical representation, depicting a decay in teleportation fidelity with respect to damping probability for a three-photon GHZ state with an amplitude coefficient value, in accordance with an embodiment of the present disclosure;
FIG. 11 illustrates an exemplary graphical representation, depicting a decay in teleportation fidelity respect to damping probability for a four-photon GHZ state with an amplitude coefficient value, in accordance with an embodiment of the present disclosure; and
FIG. 12 illustrates an exemplary flowchart depicting a method for processing multipartite entangled states under programmable noisy quantum channel conditions, in accordance with an embodiment of the present disclosure.
Further, those skilled in the art will appreciate that elements in the figures are illustrated for simplicity and may not have necessarily been drawn to scale. Furthermore, in terms of the construction of the device, one or more components of the device may have been represented in the figures by conventional symbols, and the figures may show only those specific details that are pertinent to understanding the embodiments of the present disclosure so as not to obscure the figures with details that will be readily apparent to those skilled in the art having the benefit of the description herein.
DETAILED DESCRIPTION
For the purpose of promoting an understanding of the principles of the disclosure, reference will now be made to the embodiment illustrated in the figures and specific language will be used to describe them. It will nevertheless be understood that no limitation of the scope of the disclosure is thereby intended. Such alterations and further modifications in the illustrated system, and such further applications of the principles of the disclosure as would normally occur to those skilled in the art are to be construed as being within the scope of the present disclosure. It will be understood by those skilled in the art that the foregoing general description and the following detailed description are exemplary and explanatory of the disclosure and are not intended to be restrictive thereof.
In the present document, the word “exemplary” is used herein to mean “serving as an example, instance, or illustration”. Any embodiment or implementation of the present subject matter described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.
While the disclosure is susceptible to various modifications and alternative forms, specific embodiment thereof has been shown by way of example in the drawings and will be described in detail below. It should be understood, however that it is not intended to limit the disclosure to the forms disclosed, but on the contrary, the disclosure is to cover all modifications, equivalents, and alternative falling within the scope of the disclosure.
The terms “comprises”, “comprising”, “includes”, “including” or any other variations thereof, are intended to cover a non-exclusive inclusion, such that a setup, device or method that includes a list of components or steps does not include only those components or steps but may include other components or steps not expressly listed or inherent to such setup or device or method. In other words, one or more elements in a system or apparatus proceeded by “comprises… a” does not, without more constraints, preclude the existence of other elements or additional elements in the system or method.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which this disclosure belongs. The system, methods, and examples provided herein are only illustrative and not intended to be limiting.
In the following specification and the claims, reference will be made to a number of terms, which shall be defined to have the following meanings. The singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise.
A description of an embodiment with several components in communication with each other does not imply that all such components are required. On the contrary, a variety of optional components are described to illustrate the wide variety of possible embodiments of the invention. In the following detailed description of the embodiments of the disclosure, reference is made to the accompanying drawings that form a part hereof, and in which are shown by way of illustration specific embodiments in which the disclosure may be practiced. These embodiments are described in sufficient detail to enable those skilled in the art to practice the disclosure, and it is to be understood that other embodiments may be utilized and that changes may be made without departing from the scope of the present disclosure. The following description is, therefore, not to be taken in a limiting sense.
Embodiments of the present disclosure provide a photonic quantum information processing apparatus and method for processing multipartite entangled states under programmable noisy quantum-channel conditions. Further, the apparatus may include an entangled-photon source unit configured to generate an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state. Further, the entangled photon source unit may include a coherent pump laser, at least one nonlinear optical element configured for at least one of spontaneous parametric down conversion and an equivalent probabilistic entangled-photon generation process, one or more interferometric arrangements comprising polarization-manipulation optics configured to generate polarization-entangled photon pairs with a controllable balance between logical basis components, at least one of a cascaded nonlinear processing subunit and a parallel nonlinear processing subunit configured to generate at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to noisy quantum channels. Further, a plurality of programmable amplitude-damping channel (ADC) emulators optically coupled to receive each respective qubit of the GHZ-type entangled state from the entangled photon source unit. Further, each ADC emulator may include a polarization dependent interferometric circuit with at least one variable polarization-rotation element and beam-splitting element. Further, each ADC emulator may be configured to direct different polarization components of an input photon into distinct optical paths, apply a controllable polarization rotation in each of the distinct optical paths and at least one of recombine and route resulting components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit. Further, the apparatus may include a local Pauli X control unit arranged in the optical paths between the entangled-photon source unit and the plurality of ADC emulators. Further, the local Pauli X control unit may include independently addressable polarization-rotation elements positioned upstream of the amplitude-damping channel emulators, configured to selectively implement at least one of an identity operation, a Pauli X operation on individual photons before amplitude-damping evolution, causing subset of qubits to flip corresponding to a programmable control pattern.
Further, the apparatus may include a polarization-analysis and detection subsystem optically coupled to receive photons emerging from the plurality of ADC emulators. Further, the polarization-analysis may include polarization-manipulation optics configured to realize projective measurements in multiple polarization bases, one or more beam-splitting elements for basis discrimination, an array of single-photon detectors and coincidence-counting subunit may include at least one time-tagging unit configured to register multi-fold coincidence events, coincidence-counting subunit may include at least one time-tagging unit configured to register multi-fold coincidence events. Further, the apparatus may include a controlled quantum teleportation unit optically coupled to receive photons emerging from the plurality of ADC emulators. Further, the controlled quantum teleportation unit may be configured to use the n-qubit GHZ-type entangled states as controlled quantum teleportation channels, the controlled quantum teleportation unit including, a sender unit comprising a source of single photons with polarization encoded input state to teleport and a measurement stage to perform a Bell-type joint measurement between the input state and a channel photon with a detection assembly outputting at least two classical control bits, at least one controller unit receiving a channel photon, comprises polarization-rotation optics with at least two selectable settings corresponding to an allow-teleportation condition and an abort-teleportation condition, along with a detection assembly outputting at least one classical control bit and a receiver unit to receive a channel photon, comprises polarization-analysis optics to implement Pauli corrections on the photon based on classical information received from the sender and controller modules and to measure a teleported output state.
Further, the apparatus may include a processor operatively coupled to the entangled-photon source unit, the plurality of ADC emulators, the local Pauli-X control unit, the polarization-analysis and detection subsystem, and the controlled quantum teleportation unit. Further, the processor may be configured to, set, for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators select based on a GHZ-symmetric parametrization of the output multipartite state and a target performance criterion, apply periodically, selective Pauli-X operations to a selected subset of qubits by controlling the local Pauli-X control unit. Further, the processor may be configured to reconstruct, from coincidence-count data, a density matrix of an output multipartite quantum state via quantum state tomography. Further, the processor may be configured to compute multipartite entanglement metrics for the reconstructed state and, for at least three-qubit states, to classify the state into entanglement classes comprising at least one of a Greenberger-Horne-Zeilinger (GHZ) class, a W class, biseparable class, and a separable class using a GHZ symmetric parametrization. Furthermore, the processor may be configured to compute controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers, and correlate the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise. Further the apparatus 100 may provide safe and repeatable ADC emulation using photonic qubits, enabling highly stable experiments at room temperature without cryogenic or vacuum setups, thereby reducing cost and cycle time. Further, the real-time diagnostics compute genuine multipartite concurrence and CQT fidelity, with state mapping onto GHZ, W, Biseparable, or Separable classifications and continuous plots of concurrence and GHZ-plane coordinates, offering insights beyond conventional simulations. Further, the closed-form analytic schedules for NOT flips supply ready-made strategies to mitigate entanglement decay and optimize CQT fidelity, allowing tuning of quantum states prior to deployment. Furthermore, the modular and integrable design, including Displaced Sagnac Interferometers, on-chip micro-ring photon sources, and electro-optic polarization rotators, miniaturizes the apparatus into a plug-in module suitable for embedding within larger photonic systems for field use.
Referring now to the drawings, and more particularly to FIGs. 1 through FIG. 12 where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments, and these embodiments are described in the context of the following exemplary system and/or method.
FIG. 1 illustrates an exemplary block diagram representation of a photonic quantum information processing apparatus 100, in accordance with an embodiment of the present disclosure. In an embodiment, the photonic quantum information processing apparatus 100 (interchangeably referred to as the apparatus 100) may include an entangled-photon source unit 102, a plurality of local Pauli X control units 104, a plurality of programmable amplitude-damping channel (ADC) emulators 106 (interchangeably referred to as plurality of ADC emulators, ADC emulators and each ADC emulator), a polarization-analysis and detection subsystem 108 (interchangeably referred to Quantum State Tomography and QST), controlled quantum teleportation units 110 (interchangeably referred to as CQT unit), and a processor 112.
In an embodiment, the entangled-photon source unit 102 may be configured to generate one or more entangled photon pairs and/or other polarization-encoded quantum states using a coherent pump laser 114, a nonlinear optical element 116, and polarization manipulation optics 118. In some embodiments, the entangled-photon source unit 102 may further include a cascaded nonlinear processing sub-unit 120A and/or a parallel nonlinear processing sub-unit 120B for enhancing source flexibility, state quality, or generation efficiency. The processor 112 may be operatively coupled to the entangled-photon source unit 102 and may control operation of the coherent pump laser 114, timing of photon generation, and one or more source parameters associated with the nonlinear optical element 116 and the polarization manipulation optics 118. The polarization manipulation optics 118 may include, but not limited to, polarizing beam splitters (PBSs), mirrors, and half-wave plates (HWPs), and the like. In some embodiments, the processor 112 may provide closed-loop control based on measurement feedback received from one or more downstream subsystems. The plurality of local Pauli X control units 104 may be configured to selectively apply Pauli-X transformations, polarization flips, or equivalent state mappings to one or more photons, qubits, or qudit-encoded polarization states. Each local Pauli X control unit 104 may include one or more addressable polarization rotators 122 configured to receive control instructions from the processor 112 and to selectively rotate a polarization state between orthogonal basis states.
In some embodiments, the processor 112 may address each local Pauli X control unit 104 independently such that different quantum channels, protocol branches, or measurement paths are selectively transformed. The addressability of the polarization rotators 122 may enable configurable state preparation, conditional routing, error emulation, and/or protocol-specific preprocessing. The plurality of programmable amplitude-damping channel emulators 106 may be configured to emulate one or more amplitude-damping channel characteristics in a photonic domain. Each ADC emulator 106 may include an interferometric circuit 124, a polarization rotation element 126, and a beam splitting element 128, arranged to create an effective lossy quantum channel, controllable attenuation profile, or probabilistic state evolution corresponding to an amplitude-damping process .
In some embodiments, the processor 112 may program each ADC emulator 106 to emulate a respective damping parameter, damping rate, or channel strength. The ADC emulator 106 may be configured to operate in a tunable manner so that a plurality of different quantum noise conditions may be reproduced for testing, calibration, training, or state-transfer analysis. The polarization-analysis and detection subsystem 108 may be configured for quantum state tomography and may include polarization manipulation optics 130, beam splitters 132, single-photon detectors 134, and a counting subunit 136. The polarization-analysis and detection subsystem 108 may obtain measurement outcomes corresponding to different polarization bases and may generate count statistics for reconstructing a quantum state, estimating fidelity, or evaluating protocol performance.
The processor 112 may receive measurement data from the counting subunit 136 and may determine one or more state parameters based on the measured detector counts. In some embodiments, the processor 112 may compare reconstructed state information with expected state information to evaluate the performance of the entangled-photon source unit 102, the local Pauli X control units 104, and the ADC emulators 106. The controlled quantum teleportation (CQT) units 110 may include a sender unit 138, a controller unit 140, and a receiver unit 142. The sender unit 138 may be configured to prepare or encode a quantum state to be teleported, the controller unit 140 may be configured to enable, disable, or condition teleportation based on a control policy, and the receiver unit 142 may be configured to reconstruct the teleported state based on measurement information and control signals.
In some embodiments, the controlled quantum teleportation units 110 may communicate with the processor 112 to synchronize quantum state preparation, transmission, and reconstruction. The controlled quantum teleportation units 110 may be used to validate state transfer through the entangled-photon source unit 102 and to assess the effect of the programmable amplitude-damping channel emulators 106 on teleportation performance. The processor 112 may be communicatively coupled to the entangled-photon source unit 102, the plurality of local Pauli X control units 104, the plurality of ADC emulators 106, the polarization-analysis and detection subsystem 108, and the controlled quantum teleportation units 110. The processor 112 may be configured to generate control commands, coordinate timing, collect measurement data, and implement one or more classical processing operations associated with quantum information processing.
In an embodiment, the apparatus 100 may therefore provide a modular platform for generating entangled photons, selectively manipulating polarization states, emulating quantum channels, performing quantum state tomography, and executing controlled teleportation operations. The illustrated configuration of FIG. 1 is exemplary, and the relative arrangement, number, and interconnection of the components may be varied without departing from the scope of the present disclosure .
In an embodiment, the apparatus 100 may include the entangled-photon source unit 102 configured to generate an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state. Further, the entangled source unit 102 may include a coherent pump laser 114, and at least one nonlinear optical element 116 configured for at least one of spontaneous parametric down conversion and an equivalent probabilistic entangled photon generation process. Further, the entangled source unit 102 may include one or more interferometric arrangements comprising polarization-manipulation optics 118 configured to generate polarization-entangled photon pairs with a controllable balance between logical basis components. Furthermore, the entangled source unit 102 may inlcude at least one of a cascaded nonlinear processing subunit 120A and a parallel nonlinear processing subunit 120B configured to generate at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to noisy quantum channels.
Further, the plurality of programmable amplitude-damping channel (ADC) emulators 106 optically coupled to receive each respective qubit of the GHZ-type entangled state from the entangled photon source unit 102. Further, each ADC emulator 106 may include a polarization dependent interferometric circuit 124 with at least one variable polarization-rotation element 126 and beam-splitting element 128. Further, each ADC emulator 106 may be configured to direct different polarization components of an input photon into distinct optical paths, apply a controllable polarization rotation in each of the distinct optical paths and at least one of recombine and route resulting components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit.
Further, the apparatus 100 may include the plurality of local Pauli-X control units 104 arranged in the optical paths between the entangled-photon source unit 102 and the plurality of ADC emulators 106. Further, the plurality of local Pauli X control unit 104 may include independently addressable polarization-rotation elements 122 positioned upstream of the amplitude-damping channel emulators, configured to selectively implement at least one of an identity operation, a Pauli X operation and on individual photons before amplitude-damping evolution, causing subset of qubits to flip corresponding to a programmable control pattern.
Further, the apparatus 100 may include a polarization-analysis and detection subsystem 108 optically coupled to receive photons emerging from the plurality of ADC emulators 106. Further, the polarization-analysis may include polarization-manipulation optics 130 configured to realize projective measurements in multiple polarization bases, one or more beam-splitting elements 132 for basis discrimination, an array of single-photon detectors 134 and a coincidence-counting subunit 136 may include at least one time-tagging unit configured to register multi-fold coincidence events, coincidence-counting subunit may include at least one time-tagging unit configured to register multi-fold coincidence events.
Further, the apparatus 100 may include the controlled quantum teleportation unit 110 optically coupled to receive photons emerging from the plurality of ADC emulators 106. Further, the controlled quantum teleportation unit 110 may be configured to use the GHZ-type entangled states as controlled quantum teleportation channels, the controlled quantum teleportation unit 110 may include a sender unit 138 with a source of single photons with polarization encoded input state to teleport and a measurement stage to perform a Bell-type joint measurement between the input state and a channel photon. Further, the controlled quantum teleportation unit 110 may include at least one controller unit 140 to receive a channel photon with a detection assembly outputting at least two classical control bits. Further, the controlled quantum teleportation unit 110 may include polarization-rotation optics with at least two selectable settings corresponding to an allow-teleportation condition and an abort-teleportation condition, along with a detection assembly outputting at least one classical control bit and a receiver unit 142 to receive a channel photon. Further, the controlled quantum teleportation unit 110 may include polarization-analysis optics to implement Pauli corrections on the photon based on classical information received from the sender and controller modules and to measure a teleported output state.
Further, the apparatus 100 may include a processor 112 operatively coupled to the entangled-photon source unit 102, the plurality of local Pauli-X control units 104, the plurality of ADC emulators 106, the plurality of polarization-analysis and detection subsystems 108, and the plurality of controlled quantum teleportation units 110. Further, the processor 112 may be configured to, set, for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators 106 select based on a GHZ-symmetric parametrization of the output multipartite state and a target performance criterion. Further, the processor may be configured to apply periodically, selective Pauli-X operations to a selected subset of qubits by controlling the local Pauli-X control unit 104. Further, the processor may be configured to reconstruct, from coincidence-count data, a density matrix of an output multipartite quantum state via quantum state tomography through the plurality of polarisation analysis and detection subsystem 108. Further, the processor 112 may be configured to compute multipartite entanglement metrics for the reconstructed state and, for at least three-qubit states, to classify the state into entanglement classes comprising at least one of a Greenberger-Horne-Zeilinger (GHZ) class, a W class, biseparable class, and a separable class using a GHZ symmetric parametrization. Furthermore, the processor 112 may be configured to compute controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers, and correlate the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.
In an embodiment, the apparatus 100 may include subsystems realized using bulk optics and/or integrated photonics platforms. Further, the platform may primarily emulate and controls the evolution through the following set of controllable parameters, such as,
the Half-Wave Plates angle, θ_(S )∈[0,π/2] (where, the θ_(S ) ranges from 0 to π/2) to prepare the initial state using the entangled photon source unit 102;
the Half-Wave Plates with angle θ_P∈[0,π/4] (where, the θ_P ranges from 0 or π/4 to emulate amplitude-damping–like photon statistics of a matter qubit using the plurality of ADC emulators 106;
the Half-Wave Plates, θ_X∈{0,π/4} (where, the θ_(X ) is either 0 or π/4), using the local Pauli-X control unit 104 performing the population flip to decelerate the decay of entanglement, the orientations of the Quarter-Wave Plates;
the Half-Wave Plates used inside the quantum-state-tomography stage of the polarization analysis and detection unit 108; and
the angles of the Quarter-Wave Plates and Half-Wave Plates for carrying out the Controlled Quantum Teleportation protocol of the CQT unit 110.
Further, the photonic quantum information processing apparatus 100 may stimulate amplitude‐damping noise on multi-photon entangled states. Further, the apparatus 100 may generate three-photon and four-photon GHZ-type states and passes the photons through a programmable amplitude‐damping channel setup to mimic the amplitude‐damping for qubits with tuneable strength. Further, the local Pauli-X control unit 104 may include, Local Pauli σ_x (NOT) gates. Further, the NOT gates may be applied to selected photons at controlled times after GHZ-state preparation to decelerate decay of entanglement and optimize fidelity. Further, the entangled photons may be measured by single-photon detectors 134, and quantum state tomography may be performed by a polarization analysis and detection subsystem 108 to compute the type of entanglement in real time.
Further, the apparatus 100 may include, five independent control inputs such as,
(i) preparation of the initial multipartite GHZ-type state,
(ii) programmable adjustment of the amplitude-damping noise strength,
(iii) selective population flips (Pauli-X operations) applied to chosen photons to engineer photon-count statistics to faithfully reproduce the amplitude-damping behavior of matter qubits, by functioning as a safe laboratory proxy for neutral-atom or superconducting systems,
(iv) preparation of the arbitrary quantum state to be teleported inside the Alice module for both three-photon and four-photon controlled quantum teleportation (CQT) configurations, and
(v) controller-based authorization of the CQT protocol, with one Charlie module (in the three-photon setup) or two Charlie modules (in the four-photon setup) may either enable or abort the teleportation process.
Further, the NOT-gate strategy optimized for preserving entanglement, differs from the strategy optimized for preserving teleportation performance through measuring CQT fidelity. For GHZ‐type states α |0^(⊗n)⟩ +√(1-α)|1^(⊗n)⟩ with unequal amplitudes (such as, for example, |α|^2<0.5), applying NOT to all qubits tends to maximize teleportation fidelity, and applying a single NOT (on one qubit) tends to maximize GMC. Further, the apparatus 100 may enable the tuning of NOT‐gate timing and application, permitting users to independently preserve (and measure) both GMC and CQT fidelity simultaneously under the plurality of ADC emulators 106 for multiqubit.
Those skilled in the art will recognize that, for simplicity and clarity, the full structure and operation of all data processing systems suitable for use with the present disclosure are not being depicted or described herein. Instead, only so much of the photonic quantum information processing apparatus 100 as is unique to the present disclosure or necessary for an understanding of the present disclosure is depicted and described. The remainder of the construction and operation of the photonic quantum information processing apparatus 100 may conform to any of the various current implementations and practices that were known in the art.
FIG. 2 illustrates an exemplary block diagram representation of a photonic quantum information processing apparatus 100 for a three-qubit GHZ setup200 , in accordance with an embodiment of the present disclosure. Further, the photonic quantum information processing apparatus 100 for a three-qubit GHZ setup may represent photonic network architecture designed for the generation and manipulation of three-photon GHZ state. Further, the three-qubit GHZ setup may enable the state preparation for three-qubit GHZ states, emulation of amplitude damping channels (ADCs), the implementation of control operations for entanglement and CQT fidelity preservation, as well as the execution of quantum state tomography and controlled quantum teleportation.
Further, the apparatus 100 for a three-qubit GHZ 200 setup may include a plurality of local Pauli-X control units 104 referred to as Pauli X, a plurality of ADC emulators 106 referred to as ADC setup, a plurality of polarization analysis and detection subsystem 108 as QST, a controlled state teleportation unit 110 as CQT and an entangled photon source unit 102 as 3GHZ source.
Further, the apparatus 100 for a three-qubit GHZ 200 setup may implement the controlled teleportation using three-qubit GHZ‐type entangled states. Further, the controlled quantum teleportation unit 110 of the photonic quantum information processing apparatus 100 may be represented as a sender Alice (represented as the sender unit 138), a receiver Bob (represented as the receiver unit 142) and a controller Charlie (represented as the controller unit 140) . Further the sender Alice and the receiver Bob each hold one qubit of the GHZ state, and a controller Charlie may hold the remaining qubit of the GHZ state. Further, under a perfect GHZ resource, with maximally entangled, with an ideal channel without (without amplitude damping noise) with an angle,
cos〖 θ〗_s=1/√2 (where,〖 θ〗_s is an arbitrary angle)……..Equation 1
Further, Alice may perform a Bell-state measurement to produce an outcome. Further, the outcome from Alice may be sent to Bob via two classical bits c0, c1 while the controller Charlie may perform a quarter-wave-plate measurement at θ=45° (allowing teleportation) and communicate the result to Bob via one classical bit c2. Further, upon receiving the three classical bits c0, c1, c2, Bob sets the angles of the quarter-wave plate and half-wave plate accordingly to apply the required Pauli correction and reconstruct the input state with unit CQT fidelity, achieving optimal teleportation performance.
Further, the apparatus 100 for the three-qubit GHZ 200 setup may encode the shared GHZ state as a polarization-entangled photon triplet, subjects all three to independently tunable amplitude-damping noise, and enables the qubit of the controller Charlie to be measured with a quarter‐wave-plate rotation (allow teleportation θ=45°, abort teleportation θ=0°) before a detection. Further, the teleportation fidelity F may be obtained by performing polarization analysis on the photon of Bob and may compare to the input state.
Further, the apparatus may be therefore designed to enable the tuning of NOT‐gate timing and application, enabling users to preserve CQT fidelity simultaneously under the plurality of ADC emulators 106.
FIG. 3 illustrates an exemplary schematic diagram representation for the preparation of a three-qubit GHZ 200 setup of a photonic quantum information processing apparatus 100, in accordance with an embodiment of the present disclosure.
Further, the process of an entangled photon source unit 102 for the preparation of the three-qubit GHZ 200 setup may be described as follows:
In an embodiment, a grating-stabilized temperature-controlled continuous-wave laser 301 emitting light at a wavelength of around 405 nm may be directed through a half-wave plate (HWP) 302 set at an arbitrary angle 〖 θ〗_s (adjusted by the processor 112) and a focusing lens 303 may result in a pump beam with the polarization state,
|Ψ⟩=cos〖 θ〗_s |H⟩+sinθ_s |V⟩….Equation 2
Further, the temperature of the crystal and the orientation angle of HWP 302 may be regulated and adjusted by the processor 112. Further, the pump beam may pass through a dichroic mirror 304 and may be introduced into a Sagnac interferometer consisting of a polarizing beam splitter (PBS) 305, the half-wave plate (HWP) 306 adjusted to 0° and the half-wave plate (HWP) 310 adjusted to 45°, along with mirrors (307, 309). Further, the polarization components of light traveling in opposite directions within the Sagnac interferometer coherently excite a periodically poled potassium titanyl phosphate (PPKTP) crystal 308, supporting bidirectional type-II spontaneous parametric down-conversion (SPDC). Further, the described interaction produces a polarization-entangled two-photon state,
∣Ψ⟩=cosθ_s∣HV⟩+ sin θ_s∣VH⟩…..Equation 3
Further, upon leaving the Sagnac interferometer via the PBS 305, one photon passes through the dichroic mirror 311 to create the first output channel (I), while the other photon may be transmitted through dichroic mirror 304 towards the mirror 312 and may be redirected by mirror 313 through a dichroic mirror 314 into a second Sagnac interferometer containing a periodically poled lithium niobate (PPLN) waveguide crystal 318. Further, the secondary interferometer may be equipped with a PBS 315, a half-wave plate (HWP) 316 positioned at 45° and another half-wave plate (HWP) 321 positioned at 0° and mirrors (317, 319, 320) to enable bidirectional pumping of the type-0 PPLN waveguide. Further, the two photons produced during type-0 SPDC may be extracted via dichroic mirrors 322 and 323, to establish output channels (II) and (III), respectively. Further, the photon generated in the type-0 SPDC process from output channels II and III and the photon form output channel I together, produce the three-photon Greenberger–Horne–Zeilinger (GHZ) state,

∣〖GHZ〗_3⟩=cos θ_s ∣HHH⟩+sin θ_s ∣VVV⟩……..Equation 4
Further, each of the three photos produced by the grating-stabilized temperature-controlled continuous-wave laser 301 (referred to as the entangled photon source unit 102) may be sent to a plurality of displaced Sagnac Interferometer (DSI) (referred to as a plurality of programmable amplitude-damping channel (ADC) emulators 106 as shown in FIG. 4.
In an embodiment, the entangled photon source unit 102 may include the one or more bidirectionally pumped interferometer including a sagnac-type interferometer and one or more periodically poled potassium titanyl phosphate crystal configured to generate polarization entangled photon pairs. Further, the entangled photon source unit 102 may include optionally a second non-linear stage pumped by one photon of the polarized-entangled pairs to generate at least one of the three-photon GHZ-type entangled state and the four-photon GHZ-type entangled state.
In an embodiment, each of the plurality of programmable amplitude-damping channel (ADC) emulators 106 may include a displaced Sagnac interferometer configured to manage a horizontal polarization input in a first spatial mode and to convert a vertical polarization input into a mixture of a vertical component remaining in the first spatial mode and a horizontal component diverted to a second spatial mode, with the relative weight between the components controlled by the angle of the variable polarization‑rotation element 126 to realize a damping probability of the sine squared of twice an angle.
In an embodiment, independently addressable polarization‑rotation element 122 of the local Pauli‑X control unit 104 may include a local polarization rotator configured to implement an identity operation and a Pauli‑X operation on the polarization of the corresponding photon.
In an embodiment, polarization‑manipulation optics 130 of the polarization‑analysis and detection subsystem 108 may include polarization analyzers configured to realize projective measurements in at least one of a horizontal-vertical polarization basis, a diagonal-anti-diagonal polarization basis, and a right-circular-left-circular polarization basis.
In an embodiment, the sender unit 118 of the controlled quantum teleportation unit 110 may include a source of polarization-correlated photon pairs, preparation stage configured to prepare an arbitrary polarization state to be teleported, a controller unit 140 to allow or abort teleportation and measurement stage to perform a partial Bell-state measurement between the prepared state and a channel photon from the amplitude-damping channel emulator.
In an embodiment, the at least one controller unit 140 of the controlled quantum teleportation unit 110 may include the polarization-rotation optics to a first angle configured to a quarter‑wave plate settable to a first angle corresponding to an abort‑teleportation condition and a second angle corresponding to an allow‑teleportation condition, followed by a polarizing beam splitter and a plurality of single‑photon detectors.
In an embodiment, the receiver unit 142 of the controlled quantum teleportation unit 110 may include polarization-analysis optics configured to implement at least one of a identity correction, a Pauli‑X correction, a Pauli‑Z correction, and a Pauli‑Y correction on the received channel photon based on classical bits received from the sender unit 138 and the controller unit 140.
In an embodiment, the processor 112 may be configured to store reference trajectories of multipartite entanglement metrics and controlled quantum teleportation fidelity as functions of at least one of an amplitude‑damping strength, an initial GHZ-type amplitude, and a Pauli‑X control pattern. Further, the processor 112 may compare experimentally measured trajectories onto the reference trajectories in a graphical user interface to validate amplitude‑damping emulation and guide selection of Pauli‑X schedules.
FIG. 4 illustrates an exemplary schematic framework representation for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a three-qubit GHZ 200 state, in accordance with an embodiment of the present disclosure.
Further, the process of the plurality of programmable amplitude-damping channel (ADC) emulators 106 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a three-qubit GHZ state may be described as follows:
In an embodiment, the each of the three photons produced by the grating-stabilized temperature-controlled continuous-wave laser 301 (as depicted in FIG. 3) may be received by a plurality of Displaced Sagnac Interferometer (DSI) after being reflected from mirrors (402, 443, 473) and passing through a HWP (403, 444, 474) for Pauli-X (NOT) flip application, each of the HWP are at angles θ_X1,θ_X2 ,and θ_X3 respectively. Further, the each DSI may consists of a polarizing beam splitter (PBS) (404, 445, 475), a collection of mirrors (405, 408, 409, 446, 449, 450, 476, 479, 480), a HWP (406, 447, 477) positioned at a variable angle θ_P and a HWP (407, 448, 478) at 0 degrees. Further, the PBS (404, 445, 475) may separate the incoming photon into a horizontal (transmitted) and vertical (reflected) polarization components, to travel in opposite directions within the DSI. Further, the vertically polarized component (depicted by the solid line in the DSI) may be reflected by mirrors (405, 446, 476), and passes through the variable HWP (406, 447, 477) at an angle θ_P, (controlled by the software) resulting in a polarization transformation,
|V⟩→ cos 2θ_P |V⟩+sin〖 2θ〗_P |H⟩……….Equation 5
Further, upon reflection from the mirrors (408, 409, 449, 450, 479, 480), the light again strikes the PBS (404, 445, 475), and may reflect the vertical component into output mode a (as depicted by paths labelled 410, 451, 481), and may be directed towards a Beam Splitter (BS) (413, 454, 484). Further, the horizontally polarized component (as depicted by the dotted line in the DSI) may pass through a stationary HWP (407, 448, 478) set at an angle, 0° (no change in the polarization), and may be transmitted again at the PBS (404, 445, 475). Further, the component may be subsequently reflected by mirror (412, 453, 483) and directed to BS (413, 454, 484) with a probability of,
p=sin^2 (2θ_P ),……..Equation 6
defining mode b (as depicted by paths labelled 411,452,482).
Further, the entire evolution of polarization and path can therefore be expressed as,
|H⟩|a⟩→|H⟩|a⟩……….Equation 7
and
|V⟩|a⟩→√((1-p) )|V⟩|a⟩+√p|H⟩|b⟩……..Equation 8
Further, the above results may implement an Amplitude Damping Channel (ADC) mapping using polarization and spatial modes.
Further, the process of a local Pauli X control unit 104 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a three-qubit GHZ state may be described as follows:
In an embodiment, the HWPs (403, 444, 474) may be set to angular positions θ_X1,θ_X2,θ_X3, each selectable between 0° or 45°, to implement identity or qubit-flip operations as required.
Further, the process of a polarization analysis and detection subsystem 108 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a three-qubit GHZ state may be described as follows:
In an embodiment, following the DSI evolution of the three-qubit configuration, each photon, subsequent to being reflected by a mirror (412, 453, 483), may be directed towards a beam splitter (BS) (413, 454, 484). Further, the BS (413, 454, 484) may mix the two input modes with the temporal delay larger than the coherence length of the photon. Further, the BS (413, 454, 484) may probabilistically send the input photon into output paths such as, one output port may guide the photon to the polarization detection and analysis subsystem 108, and the other output port may direct to the controlled quantum teleportation (CQT) unit 110. Further, inside the polarization detection and analysis subsystem 108, the photon may pass through a quarter-wave plate (QWP) (414, 455, 485) placed at an angle, 0 degrees or 45 degrees as controlled by the processor (112), HWPs (415, 456, 486) positioned at angles 0 or 22.5 degrees as controlled by the processor (112), and a polarizing beam splitter (PBS) (416, 457, 487) to enable polarization-basis projection for performing quantum state tomography (QST). Further, with QWPs (414, 455, 485) positioned at 0 degrees and HWPs (415, 456, 486) positioned at 0 degrees, the measurements project onto horizontal polarisation, such as (∣H⟩⟨H∣). Further, the same QWPs (414, 455, 485) position at 45 degrees and HWPs (415, 456, 486) positioned at 0 degrees, the measurements project onto right-circular polarisation (∣R⟩⟨R∣), and with the same QWPs (414, 455, 485) at 45 degrees and HWPs (415, 456, 486) positioned at 22.5 degrees, the measurements may project on to diagonal polarization (∣D⟩⟨D∣).Further, the other PBS port, following the reflection from mirrors (417, 458, 488), the measurements project onto the corresponding orthogonal states which may be vertical such as, (∣V⟩⟨V∣), left-circular such as, (∣L⟩⟨L∣) and anti-diagonal such as, (∣A⟩⟨A∣) polarisations. Further, the resulting photons may be channelled towards the analysis and detection subsystem 108 through mirrors (417, 458, 488), and include, as per the following order, such as, band-pass filters (418, 419, 459, 460, 489, 490), aspheric lenses (420, 421, 461, 462, 491, 492), single-mode fibers (422, 423, 463, 464, 493, 494), and single-photon avalanche diode (SPAD) detectors (424, 425, 465, 466, 495, 496). Further, the signals may be detected and may be time-correlated with a FPGA based time-tagging unit (4104) of the counting subunit 136 for measuring coincidences.
Further, the process of a CQT unit 110 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a three-qubit GHZ state may be described as follows:
In an embodiment, the photons from one port of the beamsplitter (BS) (413, 454, 484) may be used for quantum state tomography in polarization analysis and detection subsystem 108, and the photons emerging from the other output port of the BS (413, 454, 484) may be directed to a controlled quantum teleportation (CQT) unit 110 used to teleport an arbitrary quantum state from a sender (Alice) to a receiver (Bob) under the supervision of a controller (Charlie). In an embodiment, inside, the sender (Alice), an incoming photon from the ADC emulator 106 may be directed to a BS (426), and the other input port may receive a photon generated from a heralded single-photon source. Further, a pump laser (427) operating at a wavelength for example, 810 nm may excite a periodically poled potassium titanyl phosphate (PPKTP) crystal (428) to generate polarization-correlated photon pairs in the states of the form |HV⟩ or |VH⟩, depending on the polarization of the pump beam. Further, the generated photons may be incident upon a PBS (429) configured to transmit horizontally polarized photons toward a half-wave plate (430) and may reflect vertically polarized photons towards a detection assembly including a band-pass filter (439), an aspheric lens (440), a single-mode fiber (441), a single-photon avalanche diode (442), and a field-programmable gate array (FPGA)-based time-tagging unit (4105) for coincidence counting. Further, the horizontally polarized photons transmitted toward HWP (430) may be projected onto an arbitrary polarization state (refer to Equation 2), by defining the quantum state to be teleported. Further, the BS (426) may perform a partial Bell-state measurement on photons incident from the two input ports (from BS (413) and HWP (430)), and upon projection onto selected Bell states, the photons may be directed towards a second detection assembly comprising band-pass filters (431 and 432), aspheric lenses (433 and 434), single-mode fibers (435 and 436), single-photon avalanche diodes (437 and 438), and the time-tagging unit (4105) configured for coincidence detection. Further, inside the controller (Charlie) module, a photon transmitted from BS (454) may be directed to a QWP (467), the angular orientation may determine, the teleportation protocol as enabled (QWP at 45°) or may abort (QWP at 0°). Further, the projection onto horizontal polarization aborts the protocol and projection onto circular polarization supports the teleportation from the sender (Alice) to the receiver (Bob). Further, the QWP (467) may be followed by PBS (468), band-pass filter (469), aspheric lenses (470), single-mode fibers (471), single-photon avalanche diodes (472), and the time-tagging unit (4105). Further, inside the receiver (Bob) module, the photon may be directed through a Pauli correction stage comprising a QWP (497), a HWP (498), and a PBS (499) configured to perform Pauli operations I, σ_x,σ_z and σ_y. Further, upon applying the Pauli operation may permit the Bob to retrieve the teleported state within a global phase. Further, following a PBS (499), the photons may be directed to a detection assembly comprising a band-pass filter (4100), an aspheric lens (4101), a single-mode fiber (4102), a single-photon avalanche diode (4103), and a time-tagging unit (4105) for coincidence counting.
FIG. 5 illustrates an exemplary block diagram representation of a photonic quantum information processing apparatus 100 for a four-qubit GHZ setup500 , in accordance with an embodiment of the present disclosure.
Further, the functional photonic architecture of a four-qubit GHZ setup 500may represent a photonic quantum information processing apparatus 100 designed for the generation and manipulation of four-photon GHZ state. Further, the four-qubit GHZ 500 setup may enable the state preparation for four-qubit GHZ states, emulation of amplitude damping channels (ADCs), the implementation of control operations for entanglement and CQT fidelity preservation, as well as the execution of quantum state tomography and controlled quantum teleportation.
Further, the apparatus 100 for a four-qubit GHZ 500 setup, may include a plurality of ADC emulators 106 referred to as ADC setup, a local Pauli-X control unit 104 referred to as Pauli X, a polarization detection and analysis subsystem 108 as QST, a controlled state teleportation unit 110 as CQT and an entangled photon source unit 102 as 3GHZ source.
Further, the 100 for four-qubit GHZ 500 setup, may implement the controlled quantum teleportation (CQT) using a four-qubit GHZ-type entangled channel shared among a sender (Alice), two controllers (Charlie 1 and Charlie 2), and a receiver (Bob). Further, Alice may perform a Bell-state measurement to produce an outcome. Further, the outcome from Alice may be sent to Bob via two classical bits c0, c1. In an embodiment, each controller may perform a polarization rotation as follows, such as angle, θ=45° to enable teleportation or angle, θ=0° to abort the teleportation, followed by detection, and sends one classical bit (c2 and c3) to Bob. Further, together with the two classical bits c0, c1 from Alice and the classical bits c2 and c3 for Charlie 1 and Charlie 2, the, Bob uses the four classical bits c0, c1, c2, and c3 to determine the appropriate measurement basis and to apply the required correction to the GHZ-type entangled channel photon. Further, the ideal four-qubit GHZ channel may achieve unity CQT fidelity (F=1) only as both the controllers cooperate (enable teleportation, at angle, θ=45°). Further, the four-party system may, therefore, be designed to support the tuning of NOT‐gate timing and application, enabling the users to preserve CQT fidelity simultaneously under the plurality of ADC emulators 106.
Further, for the photonic quantum information processing apparatus 100 of the three-qubit GHZ 200 setup (as shown in FIG. 2) and photonic quantum information processing apparatus 100 of the four-qubit GHZ 500 setup (as shown in FIG. 5), the photonic quantum information processing apparatus 100 may include parallel measurements of genuine multipartite concurrence (GMC) and CQT fidelity. Further, the GMC may correspond to a global entanglement measure vanishing for any separable bipartition of the GHZ state. Further, the teleportation fidelity may depend on the biseparable entanglement between Alice and Bob conditioned and averaged over the controller measurements. Further, for the three-qubit and four-qubit GHZ states under the plurality of ADC emulators 106, state trajectories may be explicitly mapped onto GHZ-symmetric representations for classification into SLOCC classes (GHZ-class, W-class, biseparable, etc.) Further, the classifications enable identification of regimes associated with nonzero GMC versus regimes associated with teleportation fidelity above classical thresholds. Further the apparatus 100 for four-qubit GHZ 500 setup leverages the key insight about maximizing GMC and maximizing fidelity constitute distinct objectives.
Further, the apparatus 100 for four-qubit GHZ 500 setup may utilize the qubit-flipping operations. Further, the application of a NOT gate to a single qubit converts entanglement sudden death to asymptotic decay, by increasing a global multipartite concurrence (GMC). Further, the application of NOT gates to all qubits may preserve the teleportation fidelity for regimes satisfying |α|² < 0.5. Further, the experimental control of the gates, including photonic polarization flip operations, may enable the calibration of a number and placement of NOT operations for optimization of respective performance metrics
Further, the dual control enables execution of multiple experiments within a common experimental configuration using different NOT gate strategies, by permitting direct comparison of corresponding GMC values and teleportation fidelities. Further, the apparatus 100 for four-qubit GHZ 500 setup may include circuitry configured to compute a global multipartite concurrence (GMC) from measured density matrices obtained via quantum state tomography. Further, the circuitry further computes teleportation fidelity,
F =⟨Ψ_in |ρ_out | Ψ_in⟩……….Equation 9
Where, (ρ_out is the state obtained by Bob, Ψ_inis the state to be teleported by Alice) from output measurements.
Further, by systematically scanning the initial states, the amplitude damping channel (ADC) strength p, and the applied NOT operations, the apparatus 100 for four-qubit GHZ 500 setup may empirically optimizes both F and GMC, ensuring successful controlled quantum teleportation when F exceeds the threshold value of ⅔ ≅ 0.67.
In the preferred embodiment, the entangled GHZ qubits may be encoded in photon polarization. Further, a photonic bench (or chip) may include a probabilistic entangled photon source unit 102 (SPDC source with polarization entanglement) split into paths for Alice, Bob, and controller(s) Charlie(s). Further, the amplitude-damping noise may be emulated by controllable optical loss (Displaced Sagnac Interferometers with Half-Wave Plates) applied to each channel in the plurality of ADC Emulators 106. Further, the local NOT gates may be implemented as rapid polarization flips (half-wave plates) on selected qubits mid-stream. Further, the timing of each NOT insertion may be programmable.
FIG. 6 illustrates an exemplary schematic diagram representation for preparation of a four-qubit GHZ 500 setup of a photonic quantum information processing apparatus 100, in accordance with an embodiment of the present disclosure. Further, the process of an entangled photon source unit 102 for the preparation of the four-qubit GHZ 500 setup may be described as follows:
In an embodiment, a four-qubit GHZ state may begin with a grating-stabilized temperature-controlled continuous-wave laser source 601 operating at a wavelength around 405 nm. Further, the laser beam may be passed through a HWP 602 positioned at an angle θ_s (adjusted by the processor 112) and a focusing lens 603, resulting in a pump beam with the polarization state as expressed through the Equation 2. Further, the pump beam may be directed through a dichroic mirror 604 and then fed into a Sagnac interferometer consisting of a PBS 605, a half-wave plate 606 and another half-wave plate 610 set at angles of 0° and 45°, respectively, along with mirrors 607 and 609 to pump the periodically poled potassium titanyl phosphate (PPKTP) crystal 608. Further, the process yields a polarization-entangled photon pair described by the state as expressed through the Equation 3. Further, upon exiting the interferometer through the PBS 605, each photon moves along two identical optical paths via dichroic mirrors (604 and 611). Further, the photons may be reflected by mirrors (612, 613, and 624) into a secondary set of Sagnac interferometers through dichroic mirror (614 and 625). Further, each of the secondary interferometer may include a periodically poled lithium niobate (PPLN) waveguide crystal (618, and 629). Further, the four-qubit GHZ 600 setup may include a PBS (615, and 626), a HWP (616, and 627) set at 45° and a HWP (621, and 632) set at angle 0°, along with mirrors (617, 619, 620, 628, 630, 631). Further, the photon pairs produced in each type-0 SPDC process may be extracted through dichroic mirrors (622 and 623) and (633 and 634), by defining the output channels (I, II) and (III, IV), respectively. Further, the four photons from the two type-0 SPDC processes as obtained from the four output channels (I, II, III, IV) may generate a four-photon Greenberger–Horne–Zeilinger (GHZ) state of the form,
∣〖GHZ〗_4⟩=cos θ_s |HHHH⟩ +sin θ_s ∣VVVV⟩………….Equation 10
Further, each of the four photos produced by the entangled photon source 102 (referred to as the entangled photon source unit 102) may be sent to a plurality of displaced Sagnac Interferometer (DSI) (referred to as a plurality of programmable amplitude-damping channel (ADC) emulators 106 as shown in FIG. 7
FIG. 7 illustrates an exemplary schematic framework representation for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a four-qubit GHZ 500 state, in accordance with an embodiment of the present disclosure.
Further, the process of a plurality of programmable amplitude-damping channel (ADC) emulators 106 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a four-qubit GHZ state may be described as follows:
In an embodiment, the each of the four photons produced by the entangled photon source 102 (as depicted in FIG. 6) may be received by a plurality of Displaced Sagnac Interferometer (DSI) may be directed into a Displaced Sagnac Interferometers (DSI) by passing through HWPs (703, 744, 774, 7104). Further, from reflecting off mirrors (702, 743, 773, 7103), the photons passing through a Pauli-X (NOT) flip applying HWP (703, 744, 774, 7104) each at angles θ_X1,θ_X2 , θ_X3 and θ_X4 and further, each photon may enter a DSI. Further, the DSI may include a PBS (704, 745, 775, 7105), a set of mirrors (705, 708, 709, 746, 749, 750, 776, 779, 780, 7106, 7109, 7110), an HWP at angle, 0° (707, 748, 778, 7108), and a uniformly motorized HWP θ_P (706, 747,777, 7107). Further, the operation and adjustment of the HWPs (706, 747, 777, 7107) are controlled by the processor 112. Further, the DSIs may work similarly to the earlier description of the FIG. 4.
Further, the process of a local Pauli X control unit 104 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a four-qubit GHZ state may be described as follows:
Further, the HWPs (703, 744, 774, 7104) may be independently controlled and set at either 0° or 45° to apply corresponding single-qubit transformations. Further, the selective and programmable application of Pauli-X operations may include the adaptive mitigation of entanglement and CQT fidelity degradation during amplitude damping, by enhancing the robustness of multipartite entangled states.
Further, the process of the polarization analysis and detection subsystem 108 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a four-qubit GHZ state may be described as follows:
In an embodiment, following the interferometric evolution, all four photons may pass through polarization-basis projection optics. Further, the optics may include mirrors (717, 758, 788, 7118), Quarter Wave Plates (QWPs) (714, 755, 785, 7115) positioned at 0 degrees or 45 degrees (as controlled by the processor 112), HWPs (715, 756, 786, 7116) at 0 degrees or 22.5 degrees (as controlled by the processor 112), and PBSs (716, 757, 787, 7117). Further, the three QWP–HWP angle settings may depict exactly the same as depicted in the three-qubit QST setup. Further, the photons may be directed to the analysis and detection subsystem 108, consisting of band-pass filters (718, 719, 759, 760, 789, 790, 7119, 7120), aspheric lenses (720, 721, 761, 762, 791, 792, 7121, 7122), single-mode fibers (722, 723, 763, 764, 793, 794, 7123, 7124), and single-photon avalanche diodes (SPADs) (724, 725, 765, 766, 795, 796, 7125, 7126). Further, the detection events may be time-correlated with a FPGA based time-tagging unit (7134) of the counting subunit 136 for coincidence analysis.
Further, the process of the polarization detection and analysis subsystem 108 for the integrated simulation of an entanglement decay, mitigation strategies, and CQT protocol based on a four-qubit GHZ state may be described as follows:
Further, the four-qubit CQT setup may be similar to the three-qubit CQT setup as shown in FIG. 4 with the addition of another controller (Charlie 2). Further, the generated photons from the entangled photon source unit 102 having undergone through the plurality of ADC emulators 106, may be distributed to a sender module (Alice), a receiver module (Bob), and two controller modules (Charlie 1 and Charlie 2). Further, inside the sender (Alice) module, a pump laser (727) may be operating at approximately 810 nm and may be configured to excite a periodically poled potassium titanyl phosphate (PPKTP) crystal (728) to generate polarization-correlated photon pairs. Further, the photon pairs may be directed through a PBS (729), and one output path may be coupled to a detection assembly including a band-pass filter (739), an aspheric lens (740), a single-mode fiber (741), a single-photon avalanche diode (742), and a time-tagging unit (7135), and another output path may be directed toward a HWP (730) for preparation of a polarization-encoded quantum state (as per Equation 2). Further, the prepared photon may be combined at a BS (726) with a photon from the ADC emulator 106 to perform a partial Bell-state measurement, and the resulting outputs may be directed to another detection assembly including band-pass filters (731, 732), aspheric lenses (733, 734), single-mode fibers (735, 736), single-photon avalanche diodes (737, 738), and a time-tagging unit (7135). Further, inside a first controller module (Charlie 1), a photon from the BS (754) may be directed through a QWP (767) and a PBS (768) to implement a polarization-based control measurement (QWP at 45° enables teleportation and QWP at 0° aborts teleportation). Further, inside a second controller module (Charlie 2), a photon from BS (784) may be directed through a QWP (797) and a PBS (798) to implement an independent control measurement (QWP at 45° enables teleportation and QWP at 0° aborts teleportation). Further, the teleportation process may be permitted only upon authorization by both Charlies, corresponding to both QWPs positioned at 45 degrees. Further, inside the receiver module (Bob), the photon may be directed through a polarization analysis stage including a QWP (7127), a HWP (7128), and a PBS (7129) configured to perform Pauli operations I, σ_x,σ_z and σ_y. Further, consistent with the three-qubit case, application of Pauli operations permits Bob to retrieve the teleported state within a global phase. Further, the photon may be directed to a detection assembly including a band-pass filter (7130), an aspheric lens (7131), a single-mode fiber (7132), a single-photon avalanche diode (7133), and a time-tagging unit (7135) for coincidence counting.
FIG. 8A illustrates an exemplary graphical representation depicting an evolution of entanglement 800A of three-photon GHZ 200 state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure. In an embodiment, the processor 112 governs the experimental parameters and computational analysis. Further the processor 112 enables the Half-Wave Plate (HWP) angles θ_S for state preparation, tunes interferometric parameters through HWP θ_P, schedules NOT (Pauli-X) operations through HWP θ_X, co-ordinates the angles of the QWP(s) used by controller(s) Charlie(s) to control the teleportation, synchronizes the detection timing and projects the photon onto the desired polarization state. Further, the real-time data acquisition may be performed to record coincidence counts, and may be used to reconstruct the density matrix through the polarization detection and analysis subsystem 108. Further, from the reconstructed states, the processor 112 may compute the measures of genuine multipartite concurrence and CQT fidelity in Equation 9, from output measurements. Further, the processor 112 may also execute a detailed analysis as illustrated in Figures 8A–11. Further, the graphical representations as depicted in figures 8A and 9A may serve as reference trajectories embedded within the processor 112 for the three-photon and four-photon GHZ states, respectively. Further, each configuration of θ_S, θ_X, and θ_P may define a point on the reference trajectories, representing the position of the evolved state in the GHZ symmetric classification and tracking the entanglement evolution under damping.
Further, the three-photon GHZ state generated at the entangled photon source (as illustrated in FIG. 3), each photon may be directed through a Half-Wave Plate (HWP) (43, 444, 474) (as shown in FIG. 4) configured to perform a Pauli-X (NOT) operation. Further, the evolution of the entanglement characteristics of the states under damping may be represented as shown in the FIG. 8A. Further, all HWPs (43, 444, 474 as shown in FIG. 4) for NOT operation may be applied on the photons, oriented at 45 degrees (θ_X1=θ_X2=θ_X3=45°), the trajectories corresponding to the evolution of the states with amplitude coefficients α=√0.2,√0.4 and √0.7 (θ_S values are 63.44°, 50.77 ° and 33.21° respectively for the given α values where α=cos θ_S, as defined in Equation 2) may be represented by lines 1, 3, and 5, respectively. Further, conversely, all HWPs (43, 444, 474) (as shown in FIG. 4) may be oriented at 0 degrees (θ_X1=θ_X2=θ_X3=0°), the trajectories corresponding to the same set of amplitude coefficients are represented by lines 6, 4, and 2, respectively. Further, the analysis of lines 6 and 4 may indicate, the absence of the Pauli-X operation(θ_X1=θ_X2=θ_X3=0°), the GHZ states with α=√0.2 and α=√0.4 undergo a transition from genuine tripartite entanglement to biseparable and subsequently fully separable states, indicating rapid loss of entanglement. Further, the Pauli-X operation may be applied (θ_X1=θ_X2=θ_X3=45°), and the corresponding trajectories (lines 1 and 3) may demonstrate the same GHZ states decay sequentially from GHZ to W to biseparable and then separable, while remaining predominantly evolve in W-type and biseparable classes. Further, the described process occurs due to the application of the NOT operation mitigating the entanglement degradation during the damping process. Further, graphical representation depicting an evolution of entanglement of three-photon GHZ 800A may indicate the lines 1 and 3 to be predominantly present in the Biseparable region compared to lines 6 and 4, bringing out the application in CQT protocol as well. Further, the CQT protocol may be carried out by some Bi-separable states.
FIG. 8B illustrates an exemplary graphical representation depicting an entanglement decay with respect to damping probability 800B of a three-photon GHZ 200 state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure. Further, the FIG. 8B may include part (a), part (b) and part (c).
Further, the part (a) may include the graphical representation for entanglement decay with respect to damping probability p (as defined in Equation 6) for three-photon GHZ 200 state with, amplitude coefficient value, α=√0.2 . Further, the line 1 of the graph, represents the entanglement evolving with respect to the damping probability p when no NOT operations may be applied (θ_X1=θ_X2=θ_X3=0°). Further, the line 1 shows a sharp drop in entanglement. Further, Line 2 illustrates the evolution when NOT operations are applied to all three photons (θ_X1=θ_X2=θ_X3=45°), which shows a slower decline in entanglement. The slowest decay happens as the NOT operation may be applied to only one of the three photons and two of the three photons, as shown in lines 3 and 4, respectively.
Further, the part (b) may include the graphical representation for entanglement decay with respect to damping probability p for three-photon GHZ 200 state with, amplitude coefficient value, α=√0.4 . Further, the decay pattern of part (b) may correspond to the decay pattern of part (a).
Further, the part (c) may include the graphical representation for entanglement decay with respect to damping probability p for three-photon GHZ 200 state with, amplitude coefficient value, α=√0.7. Further, the entanglement may exhibit slower decay for a configuration without NOT operations (θ_X1=θ_X2=θ_X3= 0°; line 2) relative to a configuration with NOT operations applied to all three photons (θ_X1=θ_X2=θ_X3= 45°; line 1). Further, for the illustrated GHZ state, the optimal reduction of entanglement loss occurs under application of the NOT operation to one photon or to two photons among the three photons (lines 3 and 4 respectively), by preserving higher multipartite entanglement levels during the damping process.
FIG. 9A illustrates an exemplary graphical representation, depicting an evolution of entanglement 900A of four-photon GHZ 500 state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure. In an embodiment, the graphical representation may depict the lines 2, 4, and 6 represent the entanglement decay trajectories for states with, amplitude coefficient values, α=√0.7,√0.4 and √0.2, respectively, when no NOT operations are applied, that is, all HWPs (703,744,774,7104) as shown in the FIG. 7 are all at 0 degrees (θ_X1=θ_X2=θ_X3=θ_X4=0°). Further, the lines 5, 3, and 1 correspond to the same states under conditions of all the photons undergoing NOT operation (θ_X1=θ_X2=θ_X3=45°). Further, a standardized entanglement classification scheme for four-photon entanglement remains unavailable and is represented through figures. Therefore, it is not included in the figure the states that optimize GMC vs. the states that optimize CQT fidelity. The trajectories remain useful for interpretation of states optimizing GMC versus states optimizing CQT fidelity. Further, the no-NOT trajectories and all-NOT trajectories of the states (α=√0.7,√0.4 and √0.2) exhibit behaviour comparable to three-photon GHZ-state SLOCC classification trajectories as illustrated in FIG. 8A.
FIG. 9B illustrates an exemplary graphical representation, depicting an entanglement decay with respect to damping probability of a four-photon GHZ 500 state for various amplitude coefficient values, in accordance with an embodiment of the present disclosure. Further, the FIG. 9B may include part (a), part (b) and part (c). Further, the part (a) may include the graphical representation for entanglement decay with respect to damping probability p for four-photon GHZ 500 state with, amplitude coefficient value, α=√0.2. the part (b) may include may include the graphical representation for entanglement decay with respect to damping probability p for four-photon GHZ 500 state with, amplitude coefficient value, α=√0.4 . Furthermore, the part (c) may include may include the graphical representation for entanglement decay with respect to damping probability p for four-photon GHZ state with, amplitude coefficient value, α=√0.7.
Further, following the three-photon case, four-photon GHZ states with amplitude coefficient value, α=√0.2 and α=√0.4 , depicted as line 2, in part (a) and part (b) of the FIG. 9B may retain higher degrees of entanglement under the NOT operation. Further, amplitude coefficient value, α=√0.7 of the four-photon state may exhibit greater entanglement loss under application of Pauli-X operations to all photons, depicted as line 2 in part (c) of FIG. 9B. Further, the slowest entanglement decay for all states occurs under selective application of the NOT operation to a subset of photons (one, two, or three of the four photons with lines 3, 4, and 5, respectively, consistent across the part (a), part (b) and part (c) of FIG. 9B), indicating partial application of the Pauli-X gates provides optimal entanglement preservation for the four-photon GHZ state during damping.
FIG. 10 illustrates an exemplary graphical representation, depicting a decay in teleportation fidelity with respect to damping probability 1000 for a three-photon GHZ 200 state with an amplitude coefficient value, in accordance with an embodiment of the present disclosure. Further, the FIG. 10 may include part (a), part (b) and part (c). In an embodiment, the evolution of teleportation fidelity under amplitude damping may be analyzed for different configurations of the Half-Wave Plates (HWPs) (403, 444, 474) (as shown in FIG. 4) implementing Pauli-X (NOT) operations.
Further, for the case of application of NOT operations on all photons 〖(θ〗_X1=θ_X2=θ_X3=45°), the decay of teleportation fidelity may be significantly delayed for states with amplitude coefficients, α=√0.2, depicted as line 4, in part (a) and α=√0.4 depicted as line 4, in part (b), indicating enhanced teleportation performance. Further, the absence of NOT operations 〖(θ〗_X1=θ_X2=θ_X3=0°), depicted as line 1 in part (a) and part (b) or application of NOT operations to a subset of the three photons may result as one photon as depicted by line 2, in part (a) and part (b) or two photons as depicted by line 3, in part (a) and part (b) and may lead to faster reduction of teleportation fidelity, and the teleportation performance remains unimproved. Further, only for the amplitude coefficient value, α<√0.5, the collective application of Pauli-X gates on all three photons may improve fidelity preservation during the amplitude damping.
Further, for the GHZ state with amplitude coefficient α=√0.7 as depicted in part (c), a different behavior may be observed. Further, teleportation fidelity may decay more slowly under the absence of NOT operations, depicted by line 1 of part (c), or under application of a NOT operation to only one of the three photons, as depicted by line 2 of part (c). Further, teleportation fidelity may decrease more rapidly under amplitude damping upon application of the Pauli-X transformation to all three photons, as depicted by line 4 of part (c), or upon application of NOT operations to two of the three photons, as depicted by line 3 of part (c). Further, for the amplitude coefficient value, α>√0.5, the complete application of NOT gates does not enhance teleportation performance, and minimal or no Pauli-X intervention may enable better fidelity preservation.
FIG. 11 illustrates an exemplary graphical representation, depicting a decay in teleportation fidelity with respect to damping probability 1100 for a four-photon GHZ 500 state with an amplitude coefficient value, in accordance with an embodiment of the present disclosure. Further, the FIG. 11 may include part (a), part (b) and part (c).
Further, all the four photons undergoing the NOT operation, the decay of teleportation fidelity may be delayed for states with, amplitude coefficient value, α=√0.2 as depicted by line 5 of part (a) and amplitude coefficient value, α=√0.4 as depicted by line 5 of part (b), demonstrating improved resistance to amplitude damping compared to NOT gates applied to a subset of photons (one of the four photons as depicted by line 2 of part (a) and part (b), two of the four photons as depicted by line 3 of part (a) and part (b) and three of the four photons as depicted by line 4 of part (a) and part (b)) or the absence of NOT operation (as depicted by line 1 of part (a) and part (b). Further, for the amplitude coefficient value, α=√0.7, the slowest fidelity decay may occur under the absence of NOT operations as depicted by line 1 of part (c) compared to NOT gates applied to a subset of photons (one of the four photons as depicted by line 2 of part (c), two of the four photons as depicted by line 3 of part (c) and three of the four photons as depicted by line 4 of part (c)) or NOT operation applied to all four photons as depicted by line 5 of part (c)). Further, the GHZ states with amplitude coefficient value, α<√(0.5 ) may benefit from application of NOT operations to all photons, and the GHZ states with amplitude coefficient value, α>√0.5 may exhibit better fidelity preservation under absence of NOT operations or minimal intervention. Further, the analysis and detection subsystem 108 may perform a systematic and thorough analysis of the obtained results, enabling evaluation of the impact of NOT operations on fidelity and entanglement characteristics.
FIG. 12 illustrates an exemplary flowchart depicting a method 1200 for processing multipartite entangled states under programmable noisy quantum channel conditions, in accordance with an embodiment of the present disclosure.
At step 1202, the method 1200 includes generating, by a photonic quantum information processing apparatus 100, an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state using an entangled photon sequence from an entangled photon source unit 102. Further, the generation of the n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state may include, pumping, by the apparatus 100, at least one nonlinear optical element 116 with a coherent pump laser 114 for at least one of spontaneous parametric down conversion and an equivalent probabilistic entangled photon generation process. Further, generating, by the apparatus 100, polarization entangled photon pairs with a controllable balance between logical basis components using one or more interferometric arrangements comprising polarization manipulation optics 118. Further, the generating, by the apparatus 100, at least one of a three photon GHZ type entangled state and a four photon GHZ type entangled state corresponding to quantum communication channels using at least one of a cascaded nonlinear processing subunit 120A and a parallel nonlinear processing subunit 120B.
At step 1204, the method 1200 includes directing, by the apparatus 100, photons representing each respective qubit of the GHZ type entangled state emerging from the entangled photon source unit 102 into a corresponding one of a plurality of programmable amplitude damping channel (ADC) emulators 106. Further, optically coupling, by the apparatus 100, the plurality of programmable amplitude damping channel (ADC) emulators 106 to receive each respective qubit of the GHZ type entangled state directly from the entangled photon source unit 102.
At step 1206, the method 1200 includes directing, by the apparatus 100, in each ADC emulator 106, different polarization components of the input photon from the entangled photon source unit 102 into distinct optical paths.
At step 1208, the method 1200 includes applying, by the apparatus 100, in each distinct optical path of the ADC emulator 106, a controllable polarization rotation to the polarization components.
At step 1210, the method 1200 includes routing, by the apparatus 100, from each ADC emulator, resulting polarization components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude damping quantum channel with a tuneable decay probability for each photonic qubit.
At step 1212, the method 1200 includes arranging, by the apparatus 100, a local Pauli X control unit 104 in the optical paths between the entangled photon source unit 102 and the plurality of ADC emulators 106, and selectively implementing, using independently addressable polarization rotation elements 122 positioned upstream of the amplitude damping channel emulators, at least one of an identity operation, a Pauli X operation on individual photons of the GHZ type entangled state before the photons enter the amplitude damping channel emulators, causing a subset of qubits to flip according to a programmable control pattern.
At step 1214, the method 1200 includes routing, by the apparatus 100, from each ADC emulator, resulting polarization components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude damping quantum channel with a tuneable decay probability for each photonic qubit.
At step 1216, the method 1200 includes directing, by the apparatus 100, photons emerging from the plurality of ADC emulators 106 to a polarization analysis and detection subsystem 108, and, in the polarization analysis and detection subsystem 108.
At step 1218, the method 1200 includes directing, by the apparatus 100, a first portion of the photons emerging from the plurality of ADC emulators 106 to the polarization analysis and detection subsystem and directing a second portion of the photons emerging from the plurality of ADC emulators 106 to a controlled quantum teleportation unit, both subsystems being optically coupled to receive photons from the ADC emulators 106.
At step 1220, the method 1200 includes setting, by the apparatus (100), for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators (106) using a processor operatively coupled to the entangled-photon source unit (102), the plurality of ADC emulators, the local Pauli-X control unit (104), the polarization-analysis and detection subsystem (108), and the controlled quantum teleportation unit (110).
At step 1222, the method 1200 includes applying periodically and iteratively, by the apparatus 100, by the processor 112 via the local Pauli X control unit 104, selective Pauli X operations to a selected subset of qubits of the GHZ type entangled state propagating between the entangled photon source unit 102 and the plurality of ADC emulators 106.
At step 1224, the method 1200 includes reconstructing, by the apparatus 100, via the processor 112, from coincidence count data generated by the polarization analysis and detection subsystem 108, a density matrix of an output multipartite quantum state via quantum state tomography.
At step 1228, the method 1200 includes computing, by the apparatus 100, via the processor 112, multipartite entanglement metrics for the reconstructed density matrix and, for at least three qubit states, classifying the state into entanglement classes using a GHZ symmetric parametrization.
At step 1230, the method 1200 includes computing, by the apparatus 100, via the processor 112, controlled quantum teleportation fidelity for three qubit channels with one controller and four qubit channels with two controllers from data generated by the controlled quantum teleportation unit 110, and correlating the fidelity with the entanglement metrics and applied Pauli X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude damping noise.
In an embodiment, the method 1200 may include pumping, by the apparatus 100, at least one nonlinear optical element 116 with a coherent pump laser 114 for at least one of spontaneous parametric down-conversion and an equivalent probabilistic entangled-photon generation process. Further, the method 1200 may include generating, by the apparatus (100), polarization-entangled photon pairs with a controllable balance between logical basis components using one or more interferometric arrangements comprising polarization-manipulation optics (118). Further, the method 1200 may include generating, by the apparatus 100, at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to quantum channels using at least one of a cascaded nonlinear processing subunit 120A and a parallel nonlinear processing subunit 120B.
In an embodiment, the method 1200 may include the plurality of programmable amplitude-damping channel (ADC) emulators 106 to receive each respective qubit of the GHZ-type entangled state directly from the entangled-photon source unit 102.
In an embodiment, the method 1200 may include positioning independently, by the apparatus 100, addressable polarization-rotation elements 122 of the local Pauli-X control unit 104 upstream of the amplitude-damping channel emulators.
In an embodiment, the method 1200 the directing photons emerging from the plurality of ADC emulators 106 to the polarization-analysis and detection subsystem 108 may include realizing, by the apparatus 100, projective measurements in multiple polarization bases using polarization-manipulation optics (130). Further, the discriminating, by the apparatus 100, measurement bases using one or more beam-splitting elements 132. Further, the detecting, by the apparatus 100, photons with an array of single-photon detectors 134. Further, the recording, by the apparatus 100. Furthermore, the multi-fold coincidence events with a coincidence-counting subunit (136) including at least one time-tagging unit.
In an embodiment, the method 1200 may directing photons emerging from the plurality of ADC emulators 106 to the controlled quantum teleportation unit 110 may include providing, by the apparatus 100, in a sender unit (138), a source of single photons with polarization encoding an input state to teleport and performing a Bell-type joint measurement between the input state and a channel photon. Further, the setting, by the apparatus 100, in at least one controller unit 140 receiving a channel photon, polarization-rotation optics to at least one of an allow-teleportation condition and an abort-teleportation condition, detecting the controller photon, and outputting at least one classical control bit. Further, the implementing, by the apparatus 100, in a receiver unit 142 receiving a channel photon, Pauli corrections on the photon based on classical information received from the sender unit 142 and controller unit 140 and measuring a teleported output state.
In an embodiment, the method 1200 generating the GHZ-type entangled state may include operating, by the apparatus 100 via the entangled-photon source unit 102, a first Sagnac interferometer including a periodically poled potassium titanyl phosphate crystal pumped bidirectionally by the coherent pump laser 114 to generate polarization-entangled photon pairs. Further, the operating, by the apparatus 100, a second Sagnac interferometer comprising a periodically poled lithium niobate waveguide crystal pumped by one photon of the polarization-entangled photon pairs to generate additional photons, to generate at least one of the three-photon GHZ-type entangled state and the four-photon GHZ-type entangled state.
The order in which the method 1200 is described is not intended to be construed as a limitation, and any number of the described method blocks may be combined or otherwise performed in any order to implement the method 1200 or an alternate method. Additionally, individual blocks may be deleted from the method 1200 without departing from the spirit and scope of the ongoing description. The method 1200 describes, without limitation, the photonic quantum information processing apparatus 1200 and method for processing multipartite entangled states under programmable quantum channel conditions. A person of skill in the art will understand that method 1200 may be modified appropriately for implementation in various manners without departing from the scope and spirit of the ongoing description.
Various embodiments of the present disclosure provide a photonic quantum information processing apparatus and method for processing multipartite entangled states under programmable quantum channel conditions. The apparatus may include an entangled photon source unit configured to generate an n qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state, the entangled photon source unit comprising a coherent pump laser, at least one nonlinear optical element for at least one of spontaneous parametric down conversion and an equivalent probabilistic entangled photon generation process, and one or more interferometric arrangements comprising polarization manipulation optics to generate polarization entangled photon pairs with a controllable balance between logical basis components. Further, the entangled photon source unit may include at least one of a cascaded nonlinear processing subunit and a parallel nonlinear processing subunit to generate at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to quantum communication channels.
Further, a plurality of programmable amplitude-damping channel emulators may be optically coupled to receive each respective qubit of the GHZ-type entangled state from the entangled photon source unit, each amplitude-damping channel emulator comprising a polarization dependent interferometric circuit with at least one variable polarization-rotation element and a beam-splitting element to direct different polarization components of an input photon into distinct optical paths, apply a controllable polarization rotation, and at least one of recombine and route resulting components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit. Further, a local Pauli X control unit may be arranged in the optical paths between the entangled photon source unit and the plurality of amplitude-damping channel emulators, the local Pauli X control unit comprising independently addressable polarization-rotation elements positioned upstream of the amplitude-damping channel emulators and configured to selectively implement at least one of an identity operation, a Pauli X operation, and on individual photons before amplitude-damping evolution, causing a subset of qubits to flip according to a programmable control pattern. Further, a polarization-analysis and detection subsystem may be optically coupled to receive photons emerging from the amplitude-damping channel emulators, the polarization-analysis and detection subsystem comprising polarization-manipulation optics configured to realize projective measurements in multiple polarization bases, one or more beam-splitting elements for basis discrimination, an array of single-photon detectors, and a coincidence-counting subunit comprising at least one time-tagging unit configured to register multi-fold coincidence events.
Further, a controlled quantum teleportation unit may be optically coupled to receive photons emerging from the amplitude-damping channel emulators, the controlled quantum teleportation unit comprising a sender unit with a source of single photons with polarization encoding an input state to teleport and a measurement stage to perform a Bell type joint measurement, at least one controller unit receiving a channel photon and comprising polarization-rotation optics with at least two selectable settings corresponding to an allow-teleportation condition and an abort-teleportation condition along with a detection assembly outputting at least one classical control bit, and a receiver unit to receive a channel photon, implement Pauli corrections on the photon based on classical information received from the sender and controller modules, and measure a teleported output state. Further, a processor may be operatively coupled to the entangled photon source unit, the amplitude-damping channel emulators, the local Pauli-X control unit, the polarization-analysis and detection subsystem, and the controlled quantum teleportation unit, the processor configured to set, for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of amplitude-damping channel emulators, apply periodically selective Pauli-X operations to a selected subset of qubits by controlling the local Pauli-X control unit, reconstruct, from coincidence-count data, a density matrix of an output multipartite quantum state via quantum state tomography, compute multipartite entanglement metrics for the reconstructed state and, for at least three-qubit states, classify the state into entanglement classes comprising at least one of a Greenberger-Horne-Zeilinger (GHZ) class, a W class, biseparable class, and a separable class using a GHZ symmetric parametrization, and compute controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers, correlating the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.
The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims.
A description of an embodiment with several components in communication with each other does not imply that all such components are required. On the contrary, a variety of optional components are described to illustrate the wide variety of possible embodiments of the invention. When a single device or article is described herein, it will be apparent that more than one device/article (whether they cooperate) may be used in place of a single device/article. Similarly, where more than one device or article is described herein (whether or not they cooperate), it will be apparent that a single device/article may be used in place of the more than one device or article or a different number of devices/articles may be used instead of the shown number of devices or programs. The functionality and/or the features of a device may be alternatively embodied by one or more other devices which are not explicitly described as having such functionality/features. Thus, other embodiments of the invention need not include the device itself.
The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope and spirit of the disclosed embodiments. Also, the words “comprising”, “having”, “containing”, and “including”, and other similar forms are intended to be equivalent in meaning and be open-ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural references unless the context clearly dictates otherwise.
Finally, the language used in the specification has been principally selected for readability and instructional purposes, and it may not have been selected to delineate or circumscribe the inventive subject matter. It is therefore intended that the scope of the invention be limited not by this detailed description, but rather by any claims that issue on an application based here on. Accordingly, the embodiments of the present invention are intended to be illustrative, but not limiting, of the scope of the invention, which is set forth in the following claims.
ADVANTAGES OF THE PRESENT DISCLOSURE
The present disclosure may be useful for securing quantum networks, for conditional access to quantum information with supervisory controllers. The GHZ‐based CQT channel may be directly relevant to quantum secret sharing for multiuser GHZ channels and distributed sensing. By providing a configurable setup, the apparatus 100 may accelerate development and testing of secure multiparty protocols (e.g. secret sharing, multiparty conferencing) under realistic loss. For instance, multiparty “(n,m)-type” teleportation of shared secrets has been proposed for amplitude-damping channels and the apparatus 100 may realize and optimize such schemes on a hardware. Further, the present disclosure has strong industrial potential for quantum network prototyping, as an accelerator for new quantum internet architectures.
Further, the present disclosure has broad applications in the field of quantum networking and secure communications. Further, the controlled teleportation protocols may be envisioned as primitives for future quantum networks, with information transfer requiring authorization from controllers. The present disclosure prototypes the conditional networks for example, may simulate scenarios such an adversarial or suspicious controller withholds cooperation. Further, the apparatus 100 of the present disclosure tests the thresholding schemes requiring n−2 of n controllers to unlock teleportation. Further, the use of GHZ channels connects directly to quantum secret sharing and conference key distribution, as multipartite entanglement ensures, no subset of parties recover a secret without full cooperation.
Further, the configurable setup of the apparatus 100, may accelerate the research and development of protocols. Further, the network designers may inject realistic loss and apply the NOT‐gate mitigation to verify protocol robustness before deploying expensive hardware. Further, the apparatus 100 of the present disclosure with NOT‐gate mitigation may optimize teleportation fidelity. Further, the apparatus 100 may serve as a testbed for any CQT, secret-sharing, or distributed sensing task, enabling value to the industry for accelerating new quantum network standards and for training algorithms that manage entanglement resources in networks. The following advantages may include:
The apparatus 100 of the present disclosure uses photonic qubits, providing highly stable experiments at room temperature and straightforward implementation. No cryogenic or vacuum setups required during testing, reducing cost and cycle time compared to matter-qubit experiments tests.
The apparatus 100 computes genuine multipartite concurrence and CQT fidelity on the fly. Further, by mapping the states onto the GHZ or W or Biseparable or Separable classification, the users may immediately pursue the entanglement “type” of the multi-photon entangled state during the evolution. Further, the quantification (continuous plots of concurrence, GHZ-plane coordinates) may provide insights beyond the capabilities of conventional simulations.
Further, the apparatus 100 may include the schedules for NOT flips provided for convenient implementation. Further, the schedules supply ready-made strategies to mitigate entanglement decay or optimize CQT fidelity. Furthermore, the experimenters may use the schedules to tune quantum states prior to deployment on quantum hardware.
All the components selected for may be implemented with integrated photonics. Further, the core ADC emulator and interferometers built from Displaced Sagnac Interferometers. Further, on-chip micro-ring photon sources and electro-optic polarization rotators miniaturize the apparatus 100 into a plug-in module, enabling users to embed the design within larger photonic systems for field use.
, Claims:CLAIMS
We claim:
1. A photonic quantum information processing apparatus (100) for processing multipartite entangled states under programmable noisy quantum-channel conditions, comprising:
an entangled-photon source unit (102) configured to generate an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state, the entangled-photon source unit (102) comprising:
a coherent pump laser (114);
at least one nonlinear optical element (116) configured for at least one of spontaneous parametric down-conversion and an equivalent probabilistic entangled-photon generation process;
one or more interferometric arrangements comprising polarization-manipulation optics (118) configured to generate polarization-entangled photon pairs with a controllable balance between logical basis components; and
at least one of a cascaded nonlinear processing subunit (120A) and a parallel nonlinear processing subunit (120B) configured to generate at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to noisy quantum channels;
a plurality of programmable amplitude-damping channel (ADC) emulators (106) optically coupled to receive each respective qubit of the GHZ-type entangled state from the entangled-photon source unit (102), each ADC emulator comprising a polarization-dependent interferometric circuit (124) with at least one variable polarization-rotation element (126) and beam-splitting element (128), configured to:
direct different polarization components of an input photon into distinct optical paths;
apply a controllable polarization rotation in each of the distinct optical paths; and
at least one of recombine and route resulting components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit;
a plurality of local Pauli-X control units (104) arranged in the optical paths between the entangled-photon source unit (102) and the plurality of ADC emulators (106), comprising independently addressable polarization-rotation elements (126) positioned upstream of the amplitude-damping channel emulators, configured to selectively implement at least one of an identity operation, a Pauli-X operation on individual photons before amplitude-damping evolution, causing subset of qubits to flip corresponding to a programmable control pattern;
a polarization-analysis and detection subsystem (108) optically coupled to receive photons emerging from the plurality of ADC emulators (106), comprising:
polarization-manipulation optics (130) configured to realize projective measurements in multiple polarization bases;
one or more beam-splitting elements (132) for basis discrimination;
an array of single-photon detectors (134); and
coincidence-counting subunit (136) comprising at least one time-tagging unit configured to register multi-fold coincidence events;
a controlled quantum teleportation unit (110) optically coupled to receive photons emerging from the plurality of ADC emulators (106), configured to use the n-qubit GHZ-type entangled states as controlled quantum teleportation channels, the controlled quantum teleportation unit (110) comprising:
a sender unit (138) comprising a source of single photons with polarization encoded input state to teleport and a measurement stage to perform a Bell-type joint measurement between the input state and a channel photon with a detection assembly outputting at least two classical bits;
at least one controller unit (140) receiving a channel photon, comprises polarization-rotation optics with at least two selectable settings corresponding to an allow-teleportation condition and an abort-teleportation condition, along with a detection assembly outputting at least one classical control bit; and
a receiver unit (142) to receive a channel photon, comprises polarization-analysis optics to implement Pauli corrections on the photon based on classical information received from the sender unit (138) and controller unit (140) and to measure a teleported output state;
a processor (112) operatively coupled to the entangled-photon source unit (102), the plurality of ADC emulators (106), the local Pauli-X control unit (104), the polarization-analysis and detection subsystem (108), and the controlled quantum teleportation unit (110), wherein the processor (112) is configured to:
set, for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators (106) select based on a GHZ-symmetric parametrization of the output multipartite state and a target performance criterion;
apply periodically, selective Pauli-X operations to a selected subset of qubits by controlling the local Pauli-X control unit (104);
reconstruct, from coincidence-count data, a density matrix of an output multipartite quantum state via quantum state tomography;
compute multipartite entanglement metrics for the reconstructed state and, for at least three-qubit states, to classify the state into entanglement classes using a GHZ symmetric parametrization; and
compute controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers, and correlate the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.
2. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the entangled‑photon source unit (102) comprises:
one or more bidirectionally interferometer comprising a sagnac-type interferometer and one or more periodically poled potassium titanyl phosphate crystal configured to generate polarization entangled photon pairs; and
optionally a second non-linear stage pumped by one photon of the polarized-entangled pairs to generate at least one of the three-photon GHZ-type entangled state and the four-photon GHZ-type entangled state.
3. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein each amplitude‑damping channel emulator comprises:
a displaced Sagnac interferometer configured to manage a horizontal polarization input in a first spatial mode and to convert a vertical polarization input into a mixture of a vertical component remaining in the first spatial mode and a horizontal component diverted to a second spatial mode, with the relative weight between the components controlled by the angle of the variable polarization‑rotation element (126) to realize a damping probability of the sine squared of twice an angle.
4. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein each independently addressable polarization‑rotation element (122) of the local Pauli‑X control unit (104) comprises:
a local polarization rotator configured to implement an identity operation and a Pauli‑X operation on the polarization of the corresponding photon.
5. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the polarization‑manipulation optics (130) of the polarization‑analysis and detection subsystem (108) comprise:
polarization analyzers configured to realize projective measurements in at least one of a horizontal-vertical polarization basis, a diagonal-anti-diagonal polarization basis, and a right-circular-left-circular polarization basis.
6. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the sender unit (138) of the controlled quantum teleportation unit (110) comprises:
a source of polarization-correlated photon pairs, preparation stage configured to prepare an arbitrary polarization state to be teleported, a controller unit to allow or abort teleportation and measurement stage to perform a partial Bell-state measurement between the prepared state and a channel photon from the amplitude-damping channel emulator.
7. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the at least one controller unit (140) of the controlled quantum teleportation unit (110) comprises polarization-rotation optics to a first angle:
a quarter‑wave plate settable to a first angle corresponding to an abort‑teleportation condition and a second angle corresponding to an allow‑teleportation condition, followed by a polarizing beam splitter and a plurality of single‑photon detectors.
8. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the receiver unit (142) of the controlled quantum teleportation unit (110) comprises:
polarization-analysis optics configured to implement at least one of a identity correction, a Pauli‑X correction, a Pauli‑Z correction, and a Pauli‑Y correction on the received channel photon based on classical bits received from the sender unit (138) and the controller unit (140).
9. The photonic quantum information processing apparatus (100) as claimed in claim 1, wherein the processor (112) is further configured to:
store reference trajectories of multipartite entanglement metrics and controlled quantum teleportation fidelity as functions of at least one of an amplitude‑damping strength, an initial GHZ-type amplitude, and a Pauli‑X control pattern; and
compare measured trajectories onto the reference trajectories in a graphical user interface to validate amplitude‑damping emulation and guide selection of Pauli‑X schedules.
10. A method (1200) for processing multipartite entangled states under programmable noisy quantum-channel conditions, the method (1200) comprising:
generating, by a photonic quantum information processing apparatus (100), an n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state via an entangled-photon source unit (102);
directing, by the apparatus (100), photons representing each respective qubit of the GHZ-type entangled state emerging from the entangled-photon source unit (102) into a corresponding one of a plurality of programmable amplitude-damping channel (ADC) emulators (106);
directing, by the apparatus (100), in each ADC emulator, different polarization components of the input photon from the entangled-photon source unit (102) into distinct optical paths;
applying, by the apparatus (100), in each distinct optical path of the ADC emulator (106), a controllable polarization rotation to the polarization components;
routing, by the apparatus (100), from each ADC emulator, resulting polarization components into spatial output modes corresponding to an undamped logical component and at least one of a damped logical component, for an amplitude-damping quantum channel with a tuneable decay probability for each photonic qubit;
arranging, by the apparatus (100), a local Pauli-X control unit (104) in the optical paths between the entangled-photon source unit (102) and the plurality of ADC emulators (106), and selectively implementing, using independently addressable polarization-rotation elements (126) positioned upstream of the amplitude-damping channel emulators, at least one of an identity operation, a Pauli-X operation on individual photons of the GHZ-type entangled state before the photons enter the amplitude-damping channel emulators, causing a subset of qubits to flip according to a programmable control pattern;
directing, by the apparatus (100), photons emerging from the plurality of ADC emulators (106) to a polarization-analysis and detection subsystem, and, in the polarization-analysis and detection subsystem (108);
directing, by the apparatus (100), a first portion of the photons emerging from the plurality of ADC emulators (106) to the polarization-analysis and detection subsystem and directing a second portion of the photons emerging from the plurality of ADC emulators (106) to a controlled quantum teleportation unit (110), both subsystems being optically coupled to receive photons from the ADC emulators (106);
setting, by the apparatus (100), for each qubit, an amplitude-damping strength by adjusting control parameters of the plurality of ADC emulators (106) using a processor operatively coupled to the entangled-photon source unit (102), the plurality of ADC emulators, the local Pauli-X control unit (104), the polarization-analysis and detection subsystem (108), and the controlled quantum teleportation unit (110);
applying periodically, by the apparatus (100), via the processor (112) and the local Pauli-X control unit (104), selective Pauli-X operations to a selected subset of qubits of the GHZ-type entangled state propagating between the entangled-photon source unit (102) and the plurality of ADC emulators (106);
reconstructing, by the apparatus (100), via the processor (112), from coincidence-count data generated by the polarization-analysis and detection subsystem (108), a density matrix of an output multipartite quantum state via quantum state tomography;
computing, by the apparatus (100), via the processor (112), multipartite entanglement metrics for the reconstructed density matrix and, for at least three-qubit states, classifying the state into entanglement classes using a GHZ symmetric parametrization; and
computing, by the apparatus (100), via the processor (112), controlled quantum teleportation fidelity for three-qubit channels with one controller and four-qubit channels with two controllers from data generated by the controlled quantum teleportation unit (110), and correlating the fidelity with the entanglement metrics and applied Pauli-X control patterns to identify control strategies for managing entanglement performance and teleportation performance under amplitude-damping noise.
11. The method (1200) as claimed in claim 10, wherein generating the n-qubit Greenberger–Horne–Zeilinger (GHZ) type entangled state comprises:
pumping, by the apparatus (100), at least one nonlinear optical element (116) with a coherent pump laser (114) for at least one of spontaneous parametric down-conversion and an equivalent probabilistic entangled-photon generation process;
generating, by the apparatus (100), polarization-entangled photon pairs with a controllable balance between logical basis components using one or more interferometric arrangements comprising polarization-manipulation optics (118); and
generating, by the apparatus (100), at least one of a three-photon GHZ-type entangled state and a four-photon GHZ-type entangled state corresponding to quantum communication channels using at least one of a cascaded nonlinear processing subunit (120A) and a parallel nonlinear processing subunit (120B).
12. The method (1200) as claimed in claim 10, further comprising optically coupling, by the apparatus (100), the plurality of programmable amplitude-damping channel (ADC) emulators (106) to receive each respective qubit of the GHZ-type entangled state directly from the entangled-photon source unit (102).
13. The method (1200) as claimed in claim 10, further comprising:
positioning independently, by the apparatus (100), addressable polarization-rotation elements (122) of the local Pauli-X control unit (104) upstream of the amplitude-damping channel emulators.
14. The method (1200) as claimed in claim 10, wherein directing photons emerging from the plurality of ADC emulators (106) to the polarization-analysis and detection subsystem (108) comprises:
realizing, by the apparatus (100), projective measurements in multiple polarization bases using polarization-manipulation optics (130);
discriminating, by the apparatus (100), measurement bases using one or more beam-splitting elements (132);
detecting, by the apparatus (100), photons with an array of single-photon detectors (134); and
recording, by the apparatus (100), multi-fold coincidence events with a coincidence-counting subunit (136) comprising at least one time-tagging unit.
15. The method (1200) as claimed in claim 1, wherein directing photons emerging from the plurality of ADC emulators (106) to the controlled quantum teleportation unit (110) comprises:
providing, by the apparatus (100), in a sender unit (138), a source of single photons with polarization encoding an input state to teleport and performing a Bell-type joint measurement between the input state and a channel photon;
setting, by the apparatus (100), in at least one controller unit (140) receiving a channel photon, polarization-rotation optics to at least one of an allow-teleportation condition and an abort-teleportation condition, detecting the controller photon, and outputting at least one classical control bit; and
implementing, by the apparatus (100), in a receiver unit (142) receiving a channel photon, Pauli corrections on the photon based on classical information received from the sender unit (142) and controller unit (140) and measuring a teleported output state.
16. The method (1200) as claimed in claim 10, wherein generating the GHZ-type entangled state comprises:
operating, by the apparatus (100) via the entangled-photon source unit (102), a first Sagnac interferometer comprising a periodically poled potassium titanyl phosphate crystal pumped bidirectionally by the coherent pump laser (114) to generate polarization-entangled photon pairs; and
operating, by the apparatus (100), a second Sagnac interferometer comprising a periodically poled lithium niobate waveguide crystal pumped by one photon of the polarization-entangled photon pairs to generate additional photons, to generate at least one of the three-photon GHZ-type entangled state and the four-photon GHZ-type entangled state.