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arXiv:2107.07654

Fibre polarization state compensation in entanglement-based quantum key distribution

Yicheng Shi, Hou Shun Poh, Alexander Ling, Christian Kurtsiefer

Published Jul 16, 2021• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2107.07654

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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.
Quantum key distribution – a process that encodes digital information – often utilises fibre optic technologies for commercial applications. Fibre provides the benefit of a dark channel as well as the convenience of independence of a line-of-sight connection between the sender and receiver. In order to implement quantum key distribution protocols utilising polarisation encoding, the birefringence effects of fibre must be compensated for. Birefringence is caused by manufacturing impurities in the fibre or a change in environmental conditions and results in a rotation of the state of polarisation of light as it is propagated through the fibre. With dynamic environmental conditions, the birefringence effects should be monitored with a test signal at regular time intervals so that the polarisation of each photon can be appropriately compensated to its original state. Orthogonal states are compensated simultaneously, but most protocols, such as BB84 and B92, require non-orthogonal basis sets. Instead of using a compensator for each basis, the presented scheme fixes the polarisation controller onto the plane on the Poincaré that passes through both bases, compensating both non-orthogonal bases simultaneously.
Quantum Key Distribution (QKD) employs the laws of quantum mechanics for the purpose of cryptography. Two parties, commonly called Alice and Bob, are able to share a random key which is used to encrypt a message. Any eavesdropper trying to intercept their key will have to make measurements, thereby disturbing the system. This can be detected by Alice and Bob and they will then discard their key. Polarisation encoded QKD protocols use the polarisation of single photons as qubits to generate a cryptographic key. This can be implemented using a fibre optic link between Alice and Bob but the polarisation of light is altered when passed through a fibre due to birefringence caused by asymmetries in the fibre. This causes refractive differences for orthogonal components of the state of polarisation of light, so the polarisation is rotated as the photon is transmitted through the fibre. If the fibre is fixed, the change of polarisation will be unique and constant. This can be compensated by rotating each photon appropriately to its original state. Under typical environmental conditions, such as temperature changes and vibrations, the birefringence effects vary and should be compensated in real time. Therefore, an active polarisation controller is needed in order to maintain the state of polarisation of each qubit. An investigation was done to first track how the state of polarisation changes over time in a natural environment. Both wavelength-division multiplexing and time-division multiplexing were investigated as testing methods for the compensation system. A timedivision multiplexed system was developed to compensate the changes in polarisation. Since QKD protocols such as BB84 and B92 utilise two non-orthogonal bases, two polarisation controllers are usually used for compensation. However, by using a search algorithm, one polarisation controller was able to isolate the plane on the Poincare sphere that passes through both bases, thus compensating non-orthogonal states with one device.
Long-term quantum key distribution (QKD) using polarization encoding requires a random drift compensation method. We propose a method to compensate any state of polarization based on the quantum bit error rate (QBER) of two states from two non-orthogonal mutually unbiased bases. The proposed method does not require dedicated equipment, and through a simple but highly efficient feedback loop it compensates the polarization random drift suffered by photons while transmitted over the optical fiber quantum channel. A QBER lower than 2% was observed even considering imperfect single photon detectors. Besides, we verify a 82% secret key rate generation improvement in a finite-key size BB84 implementation for a 40 km fiber-optics quantum channel.
Polarization drift due to propagation medium birefringence is a primary cause of increased quantum bit error ratio (QBER) in polarization-encoded quantum key distribution (QKD). The random nature of polarization drift and environmental instabilities cause it to vary over time, necessitating algorithms for effective polarization drift compensation in polarization-encoded optical fiber QKD links. I propose an algorithm based on processing time-multiplexed control pulses by unscented Kalman filter that minimizes the number of additional measurements that interrupt key exchange. I evaluated the robustness of the algorithm under various conditions, including random polarization drift velocities, and additional noise due to depolarization for weak-coherent BB84-like protocols, to determine the applicability limits of the proposed algorithm and its overhead.
Polarisation encoding is widely used in fibre-based Quantum Key Distribution (QKD), but random birefringence in optical fibres causes the transmitted states to drift, requiring active compensation at the receiver. Electronic Polarisation Controllers (EPCs) are commonly used for this purpose, yet the relationship between their control voltages and the resulting polarisation transformation is highly nonlinear and difficult to model. While optimisation algorithms are frequently employed to align and stabilise polarisation states, their comparative performance has not been systematically studied in realistic QKD settings. In this work, we benchmark four optimisation algorithms for electronic polarisation control, using both a numerical model and a 50 km fibre-based experimental setup. We evaluate each algorithm in terms of convergence time, failure rate, and stability, under both initial alignment and continuous drift compensation scenarios. Coordinate Descent achieved the fastest average alignment time (2.1 ms in simulation; 34.6 s experimentally), while Simulated Annealing delivered perfect reliability. We further propose a hybrid control strategy that combines fast initial alignment with high-reliability realignment. This approach was validated over a continuous 2 h QKD simulation with real fibre drift, demonstrating robust polarisation control without manual intervention. Our results provide guidance for algorithm selection in practical QKD deployments and suggest a pathway to resilient, autonomous polarisation tracking in long-distance quantum networks.