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Physical Review A

Decoy-state method of quantum key distribution with both source errors and statistics fluctuations

Huan-Hang Chi, Zong‐Wen Yu, Xiang‐Bin Wang

Published Oct 5, 2012• 16 citations
Publisher

Abstract

The effects of statistical fluctuation and vacuum source fluctuation on the decoy-state method with an unstable decoy source and signal source are studied. The method is improved by a tightened estimation of the vacuum count. Compared with the existing results with an unstable vacuum source and statistical fluctuation, the results presented here have improved the key rate of the 3-intensity protocol for quantum key distribution.

DOI
10.1103/physreva.86.042307

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The effects of statistical fluctuation and vacuum source fluctuation on the decoy-state method with an unstable decoy source and signal source are studied. The method is improved by a tightened estimation of the vacuum count. Compared with the existing results with an unstable vacuum source and statistical fluctuation, the results presented here have improved the key rate of the 3-intensity protocol for quantum key distribution.
We present an improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with a three-intensity decoy-state method. Taking the statistical fluctuations for different sources jointly, we present more tightened formulas for some key quantities used in calculating the secure final key. Numerical simulation shows that, given the total number of pulses 1012{10}^{12}1012, our method improves the key rate by about 97% for a distance of 50 km compared with the result given by Xu et al. [F. Xu et al., Phys. Rev. A 89, 052333 (2014)], and improves the key rate by 145145%145 for a distance of 100 km compared with the result from full optimization of all parameters but treating the statistical fluctuations traditionally, i.e., treating the fluctuations for different sources separately.
In order to improve the key rate of the decoy-state method, we need to jointly study yields of different bases. Given the delicate fact that pulses of the same preparation state can have different counting rates if they are measured in different bases, for example, those vacuum pulses and those single-photon pulses, existing results of decoy-state quantum key distribution using biased bases are actually flawed by assuming that they are equal. We fix this flaw through using the idea that yields of pulses prepared in different bases are the same provided that they are prepared in the same state and also measured in the same basis, for example, those single-photon pulses prepared in different bases but measured in the same basis. Based on this, we present correct formulas for the decoy-state method using biased bases. Taking the effects of statistical fluctuations into account, we then numerically study the key rates of different protocols with all parameters being fully optimized. Our result confirms the prior conclusion that the decoy-state method using biased bases can have an advantage over the symmetric protocol with unbiased bases. We obtain high key rates of our four-intensity protocol without using any vacuum source.
We present an improved formula for the lower bound of the fraction of single-photon counts in a decoy-state protocol with an unstable source. Based on the formula, we study two-intensity protocol and three-intensity protocol. The major formula in the passive two-intensity protocol proposed by Adachi, Yamamoto, Koashi, and Imoto (AYKI) [Phys. Rev. Lett. 99, 180503 (2007)] actually always holds with whatever intensity fluctuation of pump light. Therefore, the protocol can always work securely without monitoring the source state or switching the source intensity. We also show that our result can greatly improve the key rate of the three-intensity protocol with a fluctuating coherent-state source.
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.
Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution (QKD). Here, we present a general theory of the decoy state protocol based on only two decoy states and one signal state. We perform optimization on the choice of intensities of the two decoy states and the signal state. Our result shows that a decoy state protocol with only two types of decoy states---the vacuum and a weak decoy state---asymptotically approaches the theoretical limit of the most general type of decoy state protocol (with an infinite number of decoy states). We also present a one-decoy-state protocol. Moreover, we provide estimations on the effects of statistical fluctuations and suggest that, even for long-distance (larger than 100 km) QKD, our two-decoy-state protocol can be implemented with only a few hours of experimental data. In conclusion, decoy state quantum key distribution is highly practical.