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IOP Conference Series Materials Science and Engineering

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

Миронов Яков Константинович, Миронова Полина Демьяновна, Konstantin E. Rumyantsev

Published Mar 1, 2021• 2 citations
Publisher

Abstract

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.

DOI
10.1088/1757-899x/1069/1/012011

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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.
Quantum key distribution systems (QKD) provide increased security of transmitted information.For the stable operation of the QKD system, accurate synchronization of user stations isrequired with minimal time costs. An algorithm for detecting a sync signal with a threshold test isproposed. It is assumed that the sync pulse is simultaneously in two adjacent time segments. Theprobability of detecting a pair of time segments where a sync pulse is present is determined by theprobability of exceeding the threshold level by the total number of signal and noise pulses recordedin two adjacent segments. The purpose of the research is aimed at a comparative analysis of thethreshold level and probabilistic characteristics of synchronization equipment during thresholdtesting of each pair of time segments within a time frame, obtained when orienting on the Gaussand Poisson model for the number of photons and dark current pulses (DCP) received during thetime segment analysis. The probabilistic characteristics of the detection algorithm for sync signalsare studied in a quantum key distribution system based on a comparison of the number of photonsfrom an adjacent pair of time segments with a threshold level. The application of the approximationof the statistical properties of the processes at the output of the photodetector by the Poissonlaw and the normal distribution is analyzed. The influence of the Poisson and Gaussian models onthe choice of the threshold level and the calculation of the synchronization efficiency during thethreshold testing of each pair of time segments within the time frame are estimated, obtained byorientation on the Gauss and Poisson models for the number of photons and DCP received duringthe analysis of the time segment. It was established that the choice of the threshold level based onthe normal distribution gives an underestimated value. The approximation of the statistics of photonsand pulses of dark current by a normal law provides a threshold level lower than the requiredone. 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 theanalysis of the sum of counts from an adjacent pair of segments with a threshold level allow us toformulate recommendations for choosing an approximation of the signal statistics: for expresscalculations of probabilistic characteristics, it is advisable to use the Gaussian model; if a higheranalysis accuracy is required, it is recommended to use the Poisson model.
The two pass auto compensation quantum key distribution system (QKDS) with phase-encoded states of photons in synchronization mode are studied. The algorithm of synchronization QKDS, presupposing the division of the repetition period of the optical pulses on the time windows and the detection of the signal window are offered. The peculiarity of the algorithm is that it is implemented in the single-photon mode, increasing the security of synchronization mode. The second feature of the algorithm is that when equal numbers of accumulated pulses in two adjacent time windows, a decision for admission photon pulse in any of the windows, if the number of accumulated pulses in it exceeds the number of detected pulses in the other windows. In a certain algorithm in this case, both windows were “noises” that was the reason for missing the signal window. Modeling algorithm found that when the number of time windows from 2 to 1024, the difference of the limiting values of the probability does not exceed 3.34%. The requirements with respect to the duration of the time window and the photon momentum are formulated. It is shown that increasing the number of time windows from 2 to 1024 implies reducing the probability of less than 2% while maintaining the time of uncertainty in relation of emergence the photon pulse 512 times. An analytical expression for the calculation of the probability of correct detection of the signal time window in the proposed synchronization algorithm QKDS.
The parameters of the two-stage synchronization algorithm for the auto-compensation quantum key distribution (QKD) systems are investigated. The synchronization algorithm does not provide for splitting a frame equal to the period of the optical clock to the time windows. The equipment operates in the search mode for receiving a photon. The equipment goes into test mode when receiving a photon. The reception of a photon in the test mode is possible only during the action of the strobe pulse. The rest of the time the channel does not react to photons and dark current impulses (DCI). The algorithm provides for sequential testing of frames with a stop at registration of the first photon. The algorithm makes a decision about the absence of a signal after a specified number of tests. The proposed algorithm makes it possible to use single-photon avalanche photodiodes (APDs) with a significant time delay between the moments of photon reception and the restoration of APD.
A two-pass fiber-optic quantum key distribution system with phase-encoded photon states in synchronization mode has been investigated. The possibility of applying the analytical expressions for the calculation of the correct detection probability of the signal time window at synchronization has been proved. A modernized algorithm of photon pulse detection, taking into account the dead time of the single-photon avalanche photodiode was proposed. The method of engineering an optical pulse detection process during the synchronization in a quantum key distribution system has been offered.
In this article we describe the graph-analytical method for estimating single-photon synchronization parameters of an auto-compensation quantum key distribution system. In this paper is formed and described diagram of states and transitions for random search for a photon pulse with allowance for false detection. Based on the results of the analysis, expressions are defined for calculating the mathematical expectation, dispersion and average number of steps spent on the synchronization process. The interval for the average number of steps used for the synchronization process is determined. The average synchronization time according to the proposed algorithm is estimated considering the probability of false alarm. The calculations showed that the error in determining the mean synchronization time according to the expressions is no more than 1.7%. Thus, the graph-analytic method for estimating the single-photon synchronization parameters of the QKD auto-compensation system allows to determine the statistical characteristics and the average synchronization time with a low error.
Purpose of the study: development and research of an algorithm for detecting an optical signal for synchronizing stations of a quantum key distribution system with increased protection against unauthorized access. Methods of research: probability distribution, statistical analysis, single-photon detection. Results: the importance of the time synchronization process, which is implemented through high-precision detection of an optical signal, is substantiated. An optical signal detection algorithm for a synchronization method with increased protection against unauthorized access is investigated. An improved algorithm for analyzing the time domain of synchronization signal propagation using avalanche photodetectors is proposed. It is shown that the proposed algorithm allows using avalanche photodetectors in the single photon counting mode. An analysis of the time characteristics of the developed synchronization algorithm is carried out and an analytical expression for calculating the time delay of detection is presented, which provides a sequential analysis of time windows taking into account the tunable recovery time of the photodetector. The analytical expression can be used for engineering calculations when designing a QKD system. The proposed algorithm significantly reduces the likelihood of unauthorized access to the synchronization process and allows determining the time parameters of the signal window with a given accuracy, which is critical for the subsequent operation of the quantum key distribution system. Scientific novelty: an algorithm for detecting an optical signal during synchronization is proposed, which is characterized by increased protection against unauthorized access. An analytical expression for engineering calculations of the delay of detection during synchronization is presented.