Study of the characteristics of the synchronization algorithm for a quantum key distribution system based on comparing the number of samples from an adjacent pair of time windows with a threshold level

Abstract

The analysis of time and probabilistic characteristics is carried out for a two-stage synchronization algorithm in a quantum key distribution (QKD) system with automatic compensation of polarization distortions. Formulas are obtained for calculating the missing probabilities a signal pair of windows, false alarm and successful synchronization. The dependences of the missing probability a signal pair on the average number of photons and noise pulses are investigated during the analysis of a pair of windows for different threshold levels. The numerical material obtained in the course of the study indicates the possibility of using for express calculations the probability of detecting a signal pair of windows formulas oriented to the normal distribution of the number of recorded pulses at the output of a single-photon avalanche photodiode.