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arXiv:1410.3265 · Physical Review A

Statistical fluctuation analysis for measurement-device-independent quantum key distribution with three-intensity decoy-state method

Zong‐Wen Yu, Yi-Heng Zhou, Xiang‐Bin Wang

Published Mar 23, 2015• 109 citations
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Abstract

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 ${10}^{12}$, 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 $145%$ 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.

DOI
10.1103/physreva.91.032318

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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.
The performance of measurement-device-independent quantum key distribution (MDI-QKD) with different numbers of decoy-state are compared. The statistical fluctuation due to the finite length of data is considered based on the standard statistical analysis. The simulation results show that two-decoy-state method is a nearly optimal estimation in the asymptotic case. In the condition of considering statistical fluctuations, the finite length of raw key will slightly decrease the secret key rate. In all simulation cases, the key rate is maximized by optimizing the intensities of the signals. Our numerical simulation may provide valuable theoretical reference for the practical MDI-QKD experiments.
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Abstract Statistical fluctuations are unavoidable in realistic quantum key distribution (QKD) due to finite-size effect. Based on the four-intensity proposal on measurement-device-independent QKD (MDI-QKD) in [Phys. Rev. A 93 (2016) 042324], we particularly analyze the scenario that only three intensities are used, namely a three-intensity decoy-state MDI-QKD with biased basis choice. After performing full parameter optimization method, simulations results demonstrate that this scenario can obtain distinct enhancement compared with the conventional unbiased three-intensity decoy-state method, e.g. Xu et al.’s [Phys. Rev. A 89 (2014) 052333]. Furthermore, results also show that it works more efficiently by using HSPS than using WCS at longer transmission distance.
Quantum key distribution involving decoy-states is a significant application of quantum information. By using three-intensity decoy-states of single-photon-added coherent sources, we propose a practically realizable scheme on quantum key distribution which approaches very closely the ideal asymptotic case of an infinite number of decoy-states. We make a comparative study between this scheme and two other existing ones, i.e., two-intensity decoy-states with single-photon-added coherent sources, and three-intensity decoy-states with weak coherent sources. Through numerical analysis, we demonstrate the advantages of our scheme in secure transmission distance and the final key generation rate.
Reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) is a novel protocol that eliminates all possible attacks on the detector side and the necessity of reference-frame alignment in source sides. However, its performance may degrade notably due to statistical fluctuations since more parameters, e.g., yields and error rates for mismatched-basis events, must be accumulated to monitor the security. In this work, we find that the original decoy states method estimates these yields overpessimistically since it ignores the potential relations between different bases. Through jointly processing parameters of different bases, the performance of RFI-MDI-QKD is greatly improved in terms of the secret key rate and achievable distance when statistical fluctuations are considered (the statistical fluctuation analysis is the first step to the final analysis of the finite key size effect). Our results pave an avenue towards practical RFI-MDI-QKD.