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IEEE Information Technology, Networking, Electronic and Automation Control Conference (ITNEC)

Study on Statistical Analysis Method of Decoy-state Quantum Key Distribution with Finite-length Data

Wei Xiong Yu, Yuanyuan Zhou, Xuejun Zhou, Lei Wang, Shang Chen

Published May 5, 2020• 0 citations
Publisher

Abstract

In order to solve the statistical fluctuation problem caused by the finite data length in the practical quantum key distribution system, four commonly used statistical methods, DeMoivre-Laplace theorem, Chebyshev inequality, Chernoff boundary and Hoeffding boundary, are used to analyze. The application conditions of each method are discussed, and the effects of data length and confidence level on quantum key distribution security performance are simulated and analyzed. The simulation results show that the applicable conditions of Chernoff boundary are most consistent with the reality of the practical quantum key distribution system with finite-length data. Under the same experimental conditions, the secure key generation rate and secure transmission distance obtained by Chernoff boundary are better than those of the other three methods. When the data length and confidence level change, the stability of the security performance obtained by the Chernoff boundary is the best.

DOI
10.1109/itnec48623.2020.9084715

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In order to solve the statistical fluctuation problem caused by the finite data length in the practical quantum key distribution system, four commonly used statistical methods, DeMoivre-Laplace theorem, Chebyshev inequality, Chernoff boundary and Hoeffding boundary, are used to analyze. The application conditions of each method are discussed, and the effects of data length and confidence level on quantum key distribution security performance are simulated and analyzed. The simulation results show that the applicable conditions of Chernoff boundary are most consistent with the reality of the practical quantum key distribution system with finite-length data. Under the same experimental conditions, the secure key generation rate and secure transmission distance obtained by Chernoff boundary are better than those of the other three methods. When the data length and confidence level change, the stability of the security performance obtained by the Chernoff boundary is the best.
Decoy state has proven to be a very useful method of significantly enhancing the performance of a quantum key distribution (QKD) system with practical light sources. The data-set size in practical QKD protocol is always finite, which will cause statistical fluctuations. The gain and the error rate of the quantum state are analyzed by considering absolutely statistical fluctuation. The relation between key generation rate and the secure communication distance is shown with exchanged quantum signal (N = 106 -1012) by the method of two-decoy-state protocol under the condition that communication wavelength is 1310 nm (or1550 nm). The result indicates that the minimal number of exchanged quantum signals increases obviously with the increase of transmission distance. The secure transmission distance is 135 km under the condition that quantum signal is 1012.
Phase-matching quantum key distribution is a promising scheme for remote quantum key distribution, breaking through the traditional linear key-rate bound. In practical applications, finite data size can cause significant system performance to deteriorate when data size is below 1010. In this work, an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase-matching quantum key distribution, offering a new insight and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security. Moreover, we also compare the influence of the proposed improved statistical fluctuation analysis method on system performance with those of the Gaussian approximation and Chernoff–Hoeffding boundary methods on system performance. The simulation results show that the proposed scheme significantly improves the key generation rate and maximum transmission distance in comparison with the Chernoff–Hoeffding approach, and approach the results obtained when the Gaussian approximation is employed. At the same time, the proposed scheme retains the same security level as the Chernoff–Hoeffding method, and is even more secure than the Gaussian approximation.
Abstract One-decoy-state quantum key distribution with infinite length pulses can even approach the asymptotic case, i.e., infinite decoy states and infinite length pulses. Due to the limitation of experimental time, we must consider the statistical fluctuation caused by the finite number of pulses. The central limit theorem analysis method is an effective method, which can easily give the upper and lower bounds of experimental observations. Combining the central limit theorem method with the theorem that the ratio of two independent normal random variables can be approximated as a normal random variable under certain conditions, we propose a more efficient method to estimate the secure key rate. Compared with using central limit theorem method directly, our method has fewer bounds, smaller estimation deviation and higher estimation accuracy. The simulation results show that our method can significantly improve the secure key rate and transmission distance when considering statistical fluctuation and keeping the pulse number and security parameters unchanged, especially in the case of small pulse number (e.g. 107).
The statistical fluctuation problem is a critical factor in all quantum key distribution (QKD) protocols under finite-key conditions. The current statistical fluctuation analysis is mainly based on independent random samples, however, the precondition cannot always be satisfied because of different choices of samples and actual parameters. As a result, proper statistical fluctuation methods are required to solve this problem. Taking the after-pulse contributions into consideration, this paper gives the expression for the secure key rate and the mathematical model for statistical fluctuations, focusing on a decoy-state QKD protocol [Z.-C. Wei et al., Sci. Rep. 3, 2453 (2013)] with a biased basis choice. On this basis, a classified analysis of statistical fluctuation is represented according to the mutual relationship between random samples. First, for independent identical relations, a deviation comparison is made between the law of large numbers and standard error analysis. Second, a sufficient condition is given that the Chernoff bound achieves a better result than Hoeffding's inequality based on only independent relations. Third, by constructing the proper martingale, a stringent way is proposed to deal issues based on dependent random samples through making use of Azuma's inequality. In numerical optimization, the impact on the secure key rate, the comparison of secure key rates, and the respective deviations under various kinds of statistical fluctuation analyses are depicted.
Every security analysis of quantum key distribution relies on a faithful modeling of the employed quantum states. The properties of decoy state protocol based on only two decoy states and one signal state are analyzed. The performance of decoy state quantum key distribution protocol with finite resources is calculated by considering the statistical fluctuation for the yield and error rate of the quantum state. The relationship between key generation rate and transmission distance is compared by considering the data-set size to be N=108 (N=109 or N=1010 or the asymptotic case). These may provide some important parameters for the practical quantum key distribution system.
The performance of active decoy-state quantum key distribution (QKD) system with a practical light source is compared with that of passive decoy-state QKD. The effect of statistical fluctuation due to a finite data size on final secret key rate is analyzed. This procedure is based on the standard error analysis on the assumption that all the variables measured in the experiment fluctuate around their asymptotic values. The relation between key generation rate and secure transmission distance is shown with exchanged quantum efficiency of threshold detector (d=1 and d=0.4) under the condition of active decoy-state (or passive decoy-state ) QKD which we pick the data size to be N=6.0109. This analysis will provide important parameters for practical QKD experiment.