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Quantum Information Processing

Afterpulse analysis for practical phase-matching quantum key distribution

Chuan-Hao Shu, Yuhang Zhao, Zhang Wen, Meng-Rui Sun, Jian-Rong Zhu, Chun-Mei Zhang, Hong-Wei Li

Published Oct 8, 2026• 0 citations
Publisher
DOI
10.1007/s11128-026-05364-1

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In optical quantum cryptography, the afterpulse effect is important for secure key generation in quantum key distribution (QKD), because it introduces additional error and leads to great deviation from the traditional analytical model, especially for high-speed systems. This study develops a different analytical model to make QKD systems more afterpulse-compatible, by exploiting the non-Markovian nature of the afterpulse. The optimized key rate obtained here is much higher, and thus the tolerance of the afterpulse effect can be significantly improved in practical QKD systems for secure communication.
High-dimensional quantum resources provide the ability to encode several bits of information on a single photon, which can particularly increase the secret key rate rate of quantum key distribution (QKD) systems. Recently, a practical four-dimensional QKD scheme based on time-bin quantum photonic state, only with two single-photon avalanche detectors as measurement setup, has been proven to have a superior performance than the qubit-based one. In this paper, we extend the results to our proposed eight-dimensional scheme. Then, we consider two main practical factors to improve its secret key bound. Concretely, we take the afterpulse effect into account and apply a finite-key analysis with the intensity fluctuations. Our secret bounds give consideration to both the intensity fluctuations and the afterpulse effect for the high-dimensional QKD systems. Numerical simulations show the bound of eight-dimensional QKD scheme is more robust to the intensity fluctuations but more sensitive to the afterpulse effect than the four-dimensional one.