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arXiv:1308.5677 · Physical Review A

Three-intensity decoy-state method for measurement-device-independent quantum key distribution

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

Published Dec 30, 2013• 60 citations
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Abstract

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.

DOI
10.1103/physreva.88.062339

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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.
Measurement-device-independent quantum key distribution (MDI-QKD) can remove all detector loopholes. When it is combined with the decoy-state method, the final key is unconditionally secure, even if Alice and Bob do not have strict single-photon sources. However, active modulation of source intensity, which is used to generate the decoy state, may leave side channels and leak additional information to Eve. In this paper, we consider the MDI-QKD with a passive decoy state, in which both Alice and Bob send pulses to an untrusted third party, Charlie. Then, in order to estimate the key generation rate, we derive two tight formulas to estimate the lower bound of the yield and the upper bound of the error rate that both Alice and Bob send a single-photon pulse to Charlie. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account based on the standard statistical analysis.
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.
We show that the three-intensity protocol for measurement device independent quantum key distribution (MDI QKD) can be done with different light intensities in {\em only one} basis. Given the fact that the exact values yields of single-photon pairs in the XXX and ZZZ bases must be the same, if we have lower bound of the value in one basis, we can also use this as the lower bound in another basis. Since in the existing set-up for MDI-QKD, the yield of sources in different bases are normally different, therefore our method can improve the key rate drastically if we choose to only use the lower bound of yield of single-photon pairs in the advantageous basis. Moreover, since our proposal here uses fewer intensities of light, the probability of intensity mismatch will be smaller than the existing protocols do. This will further improve the advantage of our method. The advantage of using Z basis or X basis of our method is studied and significant improvement of key rates are numerically demonstrated.
Measurement-device-independent quantum key distribution (MDI-QKD) can remove all the side-channel attacks from imperfections in the detection side. However, finite-size resources undoubtedly influence its performance and the achievable finite secret key rates of MDI-QKD are typically lower than that of standard decoy-state QKD. In this paper, we introduce the efficient decoy-state method with biased basis choice into the finite-key analysis and propose a decoy-state protocol for MDI-QKD. By applying vacuum + weak decoy-state method, we analytically derive concise formulas for estimating the lower bound of single-photon yield and the upper bound of phase error rate in the case of finite resources. The simulations show that proper basis choice combined with deliberate intensity choice can substantially enhance the performance of decoy-state MDI-QKD and, without a full optimization program, our protocol can bring a long-distance implementation (168 km on standard optical fiber) of MDI-QKD with a reasonable data size of total transmitting signals (N=1015)(N={10}^{15})(N=1015).
To date, only active-decoy-state methods have been adopted in current measurement-device-independent (MDI) quantum key distribution (QKD) protocols, causing security loopholes when modulating multiple light intensities with practical devices. To solve this problem, the passive-decoy-state method will be a good choice. Until today practical passive-decoy-state MDI QKD is still missing. In this paper, based on a recently discussed structure of heralded single-photon sources, we propose a passive-decoy-state MDI QKD protocol. In present work, one does not need to modulate light sources into different intensities, but utilizes the built-in local detection events to passively generate different decoy states. Furthermore, through carrying out an appropriate mathematical method, we are able to give very precise estimations for single-photon-pair contributions. As a result, our protocol can exhibit distinct advantages compared with state-of-the-art MDI QKD schemes even when the finite-key-size effect is taken into account. Therefore, our protocol seems a promising candidate to enhance both the security and performance of MDI QKD in practical implementation.
Measurement-device-independent quantum key distribution (MDI-QKD) has been widely investigated due to its remarkable advantages on the achievable transmission distance and practical security. However, the relative low key generation rate limits its real-life implementations. In this work, we adopt the newly proposed four-intensity decoy-state scheme [Phys. Rev. A 93, 042324 (2016)] to study the performance of MDI-QKD with heralded single-photon sources (HSPS). Corresponding simulation results demonstrate that the four-intensity decoy-state scheme combining HSPS can drastically improve both the key generation rate and transmission distance in MDI-QKD, which may be very promising in future MDI-QKD systems.