PROBABILISTIC CHARACTERISTICS OF THE THRESHOLD ALGORITHM FOR DETECTING SYNCHRONIZING PULSES IN THE QUANTUM KEY DISTRIBUTION SYSTEM BASED ON INFORMATION FROM AN ADJACENT PAIR OF TIME SEGMENTS
Abstract
Quantum key distribution systems (QKD) provide increased security of transmitted information. For the stable operation of the QKD system, accurate synchronization of user stations is required with minimal time costs. An algorithm for detecting a sync signal with a threshold test is proposed. It is assumed that the sync pulse is simultaneously in two adjacent time segments. The probability of detecting a pair of time segments where a sync pulse is present is determined by the probability of exceeding the threshold level by the total number of signal and noise pulses recorded in two adjacent segments. The purpose of the research is aimed at a comparative analysis of the threshold level and probabilistic characteristics of synchronization equipment during threshold testing of each pair of time segments within a time frame, obtained when orienting on the Gauss and Poisson model for the number of photons and dark current pulses (DCP) received during the time segment analysis. The probabilistic characteristics of the detection algorithm for sync signals are studied in a quantum key distribution system based on a comparison of the number of photons from an adjacent pair of time segments with a threshold level. The application of the approximation of the statistical properties of the processes at the output of the photodetector by the Poisson law and the normal distribution is analyzed. The influence of the Poisson and Gaussian models on the choice of the threshold level and the calculation of the synchronization efficiency during the threshold testing of each pair of time segments within the time frame are estimated, obtained by orientation on the Gauss and Poisson models for the number of photons and DCP received during the analysis of the time segment. It was established that the choice of the threshold level based on the normal distribution gives an underestimated value. The approximation of the statistics of photons and pulses of dark current by a normal law provides a threshold level lower than the required one. Moreover, the difference grows with stricter requirements for the probability of false positives. The obtained probabilistic properties of the sync signal detection algorithm based on the analysis of the sum of counts from an adjacent pair of segments with a threshold level allow us to formulate recommendations for choosing an approximation of the signal statistics: for express calculations of probabilistic characteristics, it is advisable to use the Gaussian model; if a higher analysis accuracy is required, it is recommended to use the Poisson model.
