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Scientific Reports

Geometric phase-assisted single-parameter controlled phase compensation enabling quantum key distribution using phase-shifted Bell states

Ayan Kumar Nai, G. K. Samanta

Published Aug 17, 2026• 0 citations
Publisher

Abstract

Abstract Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time–polarization mapping, offering a promising route toward stable, low-QBER quantum communication.

DOI
10.1038/s41598-026-64882-1

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Optics Express•Oct 18, 2021•31 citations
Abstract Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time–polarization mapping, offering a promising route toward stable, low-QBER quantum communication.
Entanglement-based quantum key distribution (QKD) relies on the distribution of high-fidelity maximally entangled Bell states, typically generated via spontaneous parametric down-conversion (SPDC). In practical systems, unwanted relative phases arise from birefringence, pump-beam contributions, imperfect photon-pair generation, transmission through physical channels, and collection, transforming Bell states into phase-shifted states. This degrades interference visibility, increases the quantum bit error rate (QBER), and limits secure key generation. Conventional compensation techniques, such as birefringent crystals, interferometric stabilization, and spatial light modulators, are often impractical in real-world deployments. Here, we demonstrate a simple and versatile phase-compensation scheme that can be implemented at either the source or the receiver to eliminate arbitrary relative phases in Bell states. We theoretically and experimentally quantify the dependence of QBER in the BBM92 protocol on the relative phase and show that geometric-phase-based control can effectively restore entanglement quality. In a proof-of-concept experiment using a nondegenerate polarization Bell state, we achieve a fidelity exceeding 95% and reduce QBER below the 11% security threshold required for secure QKD. This robust approach enables practical phase control in entangled-photon systems and can be extended to time-bin QKD via time-polarization mapping, offering a promising route toward stable, low-QBER quantum communication.
The geometric phase, originating from the cyclic evolution of a state, such as polarization on the Poincaré sphere, is typically measured through interferometric approaches that often include unwanted contributions from the dynamic phase. Here, we present a non-interferometric technique based on quantum correlation of pair photons to measure the geometric phase of a classical beam. The transfer of geometric phase of the classical pump beam arising from the cyclic evolution of its polarization state on the Poincaré sphere onto the polarization-entangled pair photons generated via spontaneous parametric down-conversion in a Sagnac interferometer enables easy control over the quantum state. Characterization of the generated quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum state tomography, and fidelity in close agreement with theoretical predictions. We observe sinusoidal modulation of the Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell-like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric phase-based quantum gates, and compensating unwanted phase acquired by the quantum state on propagation.
ABSTRACT The geometric phase, arising from the cyclic/non‐cyclic evolution of a polarization state of light, is typically measured using interferometric methods that often introduce unwanted dynamic phase contributions. Here, we present a phase measurement technique based on the quantum correlation of pair photons to measure the geometric phase of a classical beam without any dynamic phase contribution. The transfer of the geometric phase of the classical pump beam onto polarization‐entangled pair photons generated via spontaneous parametric down‐conversion in a Sagnac interferometer scheme enables easy control over the quantum state. Characterization of the quantum states reveals that the geometric phase of the pump beam controls the coincidence counts, entanglement visibility, Bell's parameter, quantum‐state tomography, and fidelity, in close agreement with theoretical predictions. We observe sinusoidal modulation of Bell's parameter and state fidelity with changes in the geometric phase, resulting in transitions between orthogonal Bell states and Bell‐like maximally entangled states. Our results establish the geometric phase of the classical pump as a tunable parameter for quantum state control, offering a compact, passive platform for phase manipulation in quantum photonic systems, enabling geometric‐phase‐controlled quantum operations, and compensating for the unwanted phase acquired by the quantum state during propagation.
Photon-based entanglement sources, crucial for obtaining entangled states, are typically generated via spontaneous parametric down-conversion. However, birefringence in nonlinear crystals causes spatial or temporal walk-off, reducing entangled photon quality. The theoretical analysis attributes birefringent walk-off to dispersive materials curbed by pre- and post-compensation. We experimentally validate this method, enhancing polarization-entangled photon quality. We measured the Bell state along with a violation of CHSH-Bell's inequality by ∼366 standard deviations (S = 2.623 ± 0.0017). Our approach, simple and stable, does not complicate setups. Its applicability extends to optimizing various entanglement source schemes, aiding optical quantum technologies such as computation, sensing, and communication.
Quantum Key Distribution (QKD) using polarisation encoding can be hard to implement over deployed telecom fibres because the routing geometry and the birefringence of the fibre link can alter the polarisation states of the propagating photons. These alterations cause a basis mismatch, leading to an increased Quantum Bit Error Rate (QBER). In this work we demonstrate a technique for dynamically compensating fibre-induced state alteration in a QKD system over deployed fibre. This compensation scheme includes a feedback loop that minimizes the QBER using a stochastic optimization algorithm.
Quantum key distribution (QKD) using polarisation encoding can be hard to implement over deployed telecom fibres because the routing geometry and the birefringence of the fibre link can alter the polarisation states of the propagating photons. These alterations cause a basis mismatch, leading to an increased quantum bit error rate (QBER). In this work we demonstrate a technique for a dynamically compensating fibre-induced state alteration in a QKD system. This compensation scheme includes a feedback loop that minimizes the QBER using a stochastic optimization algorithm. The effectiveness of this technique is implemented and verified in a polarisation entanglement QKD system over a deployed telecom fibre.