Phase-error-rate analysis for asynchronous measurement-device-independent quantum key distribution

Abstract Quantum key distribution (QKD) is a theoretically unconditionally secure key distribution method based on quantum mechanical principles. Currently, most QKD protocols encode information in the phase domain, making the phase error rate a crucial physical parameter for evaluating protocol performance. In phase-post-selected QKD protocols, the phase error rate depends on interference measurements within non-zero phase intervals, which introduce inherent errors unrelated to eavesdropping and consequently leads to overestimation of the phase error rate. Precise analysis of phase errors can effectively reduce the protocol’s phase error rate, thereby enhancing its performance. In previous work, phase error analysis methods were primarily applied to QKD protocols under asymptotic conditions. In this study, we extend this precise phase error analysis approach to the finite-key regime of asynchronous measurement-device-independent QKD (AMDI-QKD). The performance of the original and enhanced AMDI-QKD protocols was compared under different pulse intensities through numerical simulation, and the results indicate that, compared to the original AMDI-QKD, the enhanced AMDI-QKD protocol combined with precise error analysis can extend the transmission distance by nearly 20 km and effectively reduce the phase error rate.