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Acta Physica Sinica

Analysis of statistical fluctuation in decoy state quantum key distribution system

Rongzhen Jiao, Tang Shao-Jie, Chao Zhang

Published Jan 1, 2012• 4 citations
Publisher

Abstract

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.

DOI
10.7498/aps.61.050302

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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.
The performance of active decoy-state quantum key distribution (QKD) system with an untrusted source is compared with that of passive decoy-state QKD. The key generation rate with the change of the secure transmission distance is shown under the condition of active decoy-state (or passive decoy-state) QKD where we pick the data size to be N=1012. The security characteristics of the passive scheme are studied with statistical fluctuation of the counting rate and the intensity of the practical source. At communication wavelength 1310 nm or 1550 nm, The security range of communication distance is [73.2 km, 96.5 km] or [104.5 km, 137.9 km] respectively. This analysis will provide important theoretical parameters for practical QKD experiment.
Decoy state method quantum key distribution (QKD) is one of the promising practical solutions for BB84 QKD with coherent light pulses. The number of data-set size in practical QKD protocol is always finite, which will cause statistical fluctuations. In this paper, we apply absolutely statistical fluctuation to amend the yield and error rate of the quantum state. The relationship between exchanged number of quantum signals and key generation rate is analyzed in our simulation, which offers a useful reference for experiment.
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.
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 BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and most importantly, the security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is the deviation between phase error rate of computational basis and bit error rate of dual basis. Here, we provide the rigorous and optimal analytic formula to solve the above tasks, resulting to higher secret key rate and longer secure transmission distance. Our results can be widely applied to deal with statistical fluctuation in quantum cryptography protocols.