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Chinese Physics B

Improved statistical fluctuation analysis for two decoy-states phase-matching quantum key distribution

Jiang-Ping Zhou, Yuan-Yuan Zhou, Xuejun Zhou, Xuan Bao

Published Feb 22, 2023• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1674-1056/acbdea

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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.
The decoy-state scheme is the most widely implemented quantum-key-distribution protocol in practice. In order to account for the finite-size key effects on the achievable secret key generation rate, a rigorous statistical fluctuation analysis is required. Originally, a heuristic Gaussian-approximation technique was used for this purpose, which, despite its analytical convenience, was not sufficiently rigorous. The fluctuation analysis has recently been made rigorous by using the Chernoff bound. There is a considerable gap, however, between the key-rate bounds obtained from these techniques and that obtained from the Gaussian assumption. Here we develop a tighter bound for the decoy-state method, which yields a smaller failure probability. This improvement results in a higher key rate and increases the maximum distance over which secure key exchange is possible. By optimizing the system parameters, our simulation results show that our method almost closes the gap between the two previously proposed techniques and achieves a performance similar to that of conventional Gaussian approximations.
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.
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.
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.
Recently Zhang et al [ Phys. Rev. A95, 012333 (2017)] developed a new approach to estimate the failure probability for the decoy-state BB84 QKD system when taking finite-size key effect into account, which offers security comparable to Chernoff bound, while results in an improved key rate and transmission distance. Based on Zhang et al's work, now we extend this approach to the case of the measurement-device-independent quantum key distribution (MDI-QKD), and for the first time implement it onto the four-intensity decoy-state MDI-QKD system. Moreover, through utilizing joint constraints and collective error-estimation techniques, we can obviously increase the performance of practical MDI-QKD systems compared with either three- or four-intensity decoy-state MDI-QKD using Chernoff bound analysis, and achieve much higher level security compared with those applying Gaussian approximation analysis.
In this paper, a passive decoy state phase matching quantum key distribution scheme is proposed based on the heralded pair coherent state light source to make the protocol more practical and safe. Without changing the intensity of the light source, we can derive four different data sets by dividing the raw key data into four groups according to the combined results of detectors in source end. The scheme can make use of the different data sets to estimate the parameters and extract the secret key. The key generation rate formula is derived after the parameter estimation. The performance of the proposed scheme is analyzed with and without taking statistical fluctuation into consideration. The simulation results show that compared with the existing active decoy-state method, the proposed passive method has slightly lower key rate when the transmission distance is short, and has obviously higher key rate when the transmission distance exceeds 406[Formula: see text]km. The maximum safety transmission distance of the proposed scheme is 452[Formula: see text]km which is relatively further. According to the influence of statistical fluctuation, the performance of the proposed scheme declines as the length of the data falls. Even though the data size is [Formula: see text], the max safety transmission distance is also more than 400[Formula: see text]km.