EVALUATION OF THE CHARACTERISTICS OF A TWO-STAGE SYNCHRONIZATION ALGORITHM BASED ON THE SELECTION OF AN ADJACENT PAIR OF SEGMENTS WITH THE MAXIMUM TOTAL COUNT IN THE QKD SYSTEM

Abstract

A two-stage synchronization algorithm is proposed based on the selection of an adjacent pair of
segments with the maximum total count in the QKD system. The algorithm is based on a well–known approach
to reducing the time of entering into synchronism - the analysis of adjacent pairs of time segments.
A distinctive feature of the proposed algorithm is to ensure that the probability of successful search and
testing is not worse than the required level. It should be noted that due to the testing stage, erroneous
decisions made at the search stage are rejected, which minimizes the probability of false synchronization
due to the registration of noise pulses. At the search stage, the equipment sequentially registers the total
counts from all adjacent pairs of segments. Next, a pair of segments with the maximum total count is selected,
and the count in one of the pairs of segments reliably exceeds the values of the counts from all other
pairs of segments, and the equipment proceeds to the testing stage. Testing consists of polling the
photodetector during the gating pulse to re-register the count. In case of positive testing, the process of
«rough» estimation of the moment of reception of the sync pulse is considered successfully completed,
otherwise the equipment returns to the search in the next frame. Note that the maximum allowable number
of frames and tests correspond to the search and testing stages, respectively. Analytical expressions are
obtained for calculating the time and probabilistic characteristics of the search and testing stages of the
proposed detection algorithm based on the selection of an adjacent pair of segments with the maximum
total count, including for calculating the allowable number of frames and tests while ensuring the required probabilities of successful search and testing, respectively. It has been found that with an increase in the
average number of photons in the sync pulse, the average number of frames and tests, as well as the average
time of successful search and testing, decrease significantly. For example, when the average number
of photons in a sync pulse increases by 5 times, the average number of tests for successful testing and the
average time for successful testing decrease by 1.5 times, and the permissible number of tests by 5 times.