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International Conference on Parallel, Distributed and Grid Computing (PDGC)

Graph-analytical method for estimating single photon synchronization parameters of an autocompensation quantum key distribution system

Konstantin E. Rumyantsev, Рудинский Евгений Андреевич

Published Dec 1, 2018• 2 citations
Publisher

Abstract

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.

DOI
10.1109/pdgc.2018.8745863

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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.
The time and probability parameters of the two-stage synchronization algorithm for the autocompensation quantum key distribution (QKD) systems and the analogous algorithm, implying the division of the time frame into time windows, are investigated. A comparative analysis of the parameters of synchronization algorithms is carried out and recommendations for their application for short and long fiber-optic communication lines are presented. The work also shows the methods of calculating the mean synchronization time of the QKD stations according to the above algorithms.
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.
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.
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.
A method is proposed for calculating the average time of entry into synchronism of stations of the system of quantum key distribution (QKD) with sequential polling of sections of a fiber-optic communication line (FOCL) with decreasing length. A diagram of states and transitions for a sequential search for a photon pulse is constructed. Analytical expressions are obtained for finding the probability of detecting a photon pulse, the average number of steps for entry into synchronism of stations, the variance of the number of steps and the average time for entry into connection. It is noted that when the FOCL is divided into sections with decreasing length, the level of dark current pulses (DCP) significantly decreases from section to section. The latter allows to reduce the probability of false alarms of the photodetector. The analysis of the results obtained showed that the time of entry into synchronism for the proposed algorithm is 3 times less than the time required for entry into communication of stations in the case of an algorithm-analogue. The results obtained indicate the possibility of increasing the length of the FOCL while ensuring the value of the synchronization error probability at the level of 0.01.
A two-pass auto-compensation fiber-optic quantum key distribution system (QKDS) with phase-encoded photon states in synchronization mode has been investigated. Preliminary stage sync initialization algorithm of QKDS that requires impulse-repetition period division into time windows as well as signal time window detection has been proposed. The peculiarity of the algorithm being investigated is that it is implemented in the single-photon mode which improves the synchronization mode security. The second peculiarity is that in case the number of accumulated impulses in two adjacent time windows is equal, it is decided to receive a photon impulse by any of these windows, if the number of accumulated impulses exceeds the number of registered impulses in the rest of the windows. Algorithm modeling has discovered that when the number of time windows is changed from 2 to 100000 probabilities limit values difference does not exceed 0.5 %. Requirements of time window duration ratio to the photon impulse have been formulated. It has been demonstrated that when the number of time windows is increased from 2 to 1024 the probability reduces by less than 1.5 % in case of time uncertainty decrease in respect to the photon impulse occurrence in 512 times. An analytical expression for computation of a signal time window correct detection probability in the proposed algorithm of the preliminary stage QKDS synchronization.