Optimization analysis for the maximum pairing length of mode-pairing quantum key distribution

Mode-pairing quantum key distribution (MP-QKD) circumvents the need for phase locking through post-selection pairing, still allowing it to surpass the repeaterless rate-transmittance limit. This protocol, therefore, presents a promising approach for practical QKD implementation. Without phase locking and tracking, the performance of the laser, channel, and detector critically affects the determination of the maximum pairing length <i>l</i> in pairing strategies. However, previous studies have typically set <i>l</i> based on empirical data without conducting a thorough analysis. In this study, to more accurately reflect real-world conditions, we consider fiber fluctuations, laser linewidth, laser frequency offset, and after-pulse effect to quantify the systematic misalignment determined by <i>l</i>. We employ the three-intensity decoy-state method, accounting for the finite data-size effect, to evaluate the impact of <i>l</i> in practical scenarios. Our simulation results demonstrate significant enhancements achievable through the optimal selection of <i>l</i>. Therefore, this study provides valuable insights for the advancement of future MP-QKD experiments and applications.