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Physical Review Applied

Analytical model of clock drift in quantum key distribution and a simple synchronization algorithm

L. Millet, B. Korzh, R. Thew, G. Boso

Published Sep 21, 2026• 0 citations
Publisher
DOI
10.1103/3bdt-97vf

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Clock synchronization is critical for maintaining low error rates in quantum key distribution. Here, we describe how a frequency mismatch between the transmitter and receiver clocks affects the quantum bit error rate in quantum key distribution, and derive from this model a simple synchronization algorithm together with clock stability requirements for practical operation. Our algorithm continuously compensates for both frequency mismatch and time-offset fluctuations directly from detection timestamps. It does not require a dedicated synchronization channel or auxiliary qubit sequence, converges from a large frequency mismatch within approximately one second of photon acquisition, and remains effective in low-photon-count regimes (more than 30 dB of channel loss) using standard hardware. We validate our approach by demonstrating successful key exchange over 100 km of fiber and continuous operation over 24 hours in a 16 km metropolitan network using commercial systems, with performance equivalent to using a service channel for clock synchronization.
Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users' clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice's published basis and mean photon number choices and Bob's measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of 8×10-4 and a received mean photon number of 0.01.