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Physical Review A

Tightened estimation can improve the key rate of measurement-device-independent quantum key distribution by more than 100%

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

Published May 27, 2014• 47 citations
Publisher

Abstract

We present formulas that tighten the upper bound for the phase-flip errors in the decoy-state method by using four intensities. Our result compressed the bound to about a quarter of the known result for measurement-device-independent quantum key distribution. Based on this, we find that the key rate is improved by more than 100% given weak coherent state sources, and even more than 200% with heralded single-photon sources.

DOI
10.1103/physreva.89.052325

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We present formulas that tighten the upper bound for the phase-flip errors in the decoy-state method by using four intensities. Our result compressed the bound to about a quarter of the known result for measurement-device-independent quantum key distribution. Based on this, we find that the key rate is improved by more than 100% given weak coherent state sources, and even more than 200% with heralded single-photon sources.
Tightened estimation can improve the key rate of MDI-QKD by more than 100%100\%100%
We present formulas to tightly upper bound the phase-flip errors in decoy state method by using 4 intensities. Our result compressed the bound to about a quarter of known result for MDI-QKD. Based on this, we find that the key rate is improved by more than 100%100\%100% given weak coherent state sources (WCS), and even more than 200%200\%200% with the heralded single-photon sources (HSPS).
We study the measurement-device-independent quantum key distribution (MDI-QKD) in practice with limited resources, when there are only three different states in implementing the decoy-state method. We present a tighter explicit formula to estimate the lower bound of the yield of two-single-photon pulses sent by Alice and Bob. Moreover, we show that the bounding of this yield and phase flip error of single-photon pulse pairs can be further improved by using other constraints which can be solved by a simple and explicit program. Our methods here can significantly improve the key rate and the secure distance of MDI-QKD with only three intensities.
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.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks; thus when it is combined with the decoy-state method, the final key is unconditionally secure, even if a practical weak coherent source is used by Alice and Bob. However, until now, the analysis of decoy-state MDI-QKD with a weak coherent source is incomplete. In this paper, we derive, with only vacuum+weak decoy state, some tight formulas to estimate the lower bound of yield and the upper bound of error rate for the fraction of signals in which both Alice and Bob send a single-photon pulse to the untrusted third party Charlie. The numerical simulations show that our method with only vacuum+weak decoy state can asymptotically approach the theoretical limit of the infinite number of decoy states. Furthermore, the statistical fluctuation due to the finite length of date is also considered based on the standard statistical analysis.
Parameter selection has significant influence on the performance of practical measurement-device-independent quantum key distributions. In this paper, we develop a general model for optimizing the performance of decoy-state measurement-device-independent quantum key distributions under practical experimental conditions, e.g., with finite number of pulses and including intensity fluctuations. By implementing the local search algorithm, we are able to carry out full parameter optimization within reasonable computer time. Moreover, we do calculation for the two most often used light sources, i.e., the weak coherent sources and heralded single-photon sources. Our simulation results show that the case of using heralded single-photon sources would suffer less influence from realistic conditions, exhibiting relatively better performance on both the secure key rate and secure 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.