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.