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arXiv · 2604.21388

Bayesian Phase Stabilization at the Shot-Noise Limit for Scalable Quantum Networks

Guang-Cheng Liu·Chao-Hui Xue·Fa-Xi Chen·Ming-Yang Zheng·Yi Yang·Li-Bo Li·Bin Wang·Bo-Wen Yang·Hai-Feng Jiang·Yong Wan·Ye Wang·Jiu-Peng Chen·Qiang Zhang·Jian-Wei Pan
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Abstract

High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multi-step quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of approximately 1 MHz and a duty cycle less than 6.5%, the system maintains interferometric visibility greater than 97% over fiber links of 10 km and 100 km. This phase control yields long-lived ion-ion entanglement with parity contrast exceeding 85%, enabling device-independent quantum key distribution with finite-size security analysis over 10 km and a positive asymptotic key-rate over 100 km. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it, which is a fundamental requirement for quantum repeaters. This work establishes a robust and scalable foundation for practical long-distance quantum networks.

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Guang-Cheng Liu, Chao-Hui Xue, Fa-Xi Chen, Ming-Yang Zheng, Yi Yang, Li-Bo Li, Bin Wang, Bo-Wen Yang, Hai-Feng Jiang, Yong Wan, Ye Wang, Jiu-Peng Chen, Qiang Zhang, Jian-Wei Pan. 2026-04-23. Bayesian Phase Stabilization at the Shot-Noise Limit for Scalable Quantum Networks. https://arxiv.org/abs/2604.21388

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