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arXiv:1305.7396 · Physical Review A

Practical decoy-state measurement-device-independent quantum key distribution

Shi‐Hai Sun, Ming Yuan Gao, Chunyan Li, Lin-Mei Liang

Published May 29, 2013• 65 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.87.052329

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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.
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) 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).
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.
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 rate can be obtained by estimating the gain and quantum bit error rate for various input photon numbers. In this paper, we propose to perform MDI-QKD with odd coherent state (OCS) and compare the results with weak coherent source scenario. Our simulation indicates that both the secure key rate and transmission distance can be improved evidently with OCS owing to the lower probability of multi-photon events of the OCS. Furthermore, we apply the finite key analysis to the decoy-state MDI-QKD with OCS and obtain a practical key rate.
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 safe. In this paper, we propose to perform MDI-QKD with odd coherent state (OCS) and compare the results with weak coherent source scenario. Our simulation indicates that both the secure key rate and transmission distance can be improved evidently with OCS owing to the lower probability of multi-photon events of the OCS. Furthermore, we apply the finite key analysis to the decoy state MDI-QKD with OCS and obtain a practical key rate.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to detector side channel attacks, which is a notorious security loophole problem in QKD. Importantly, both finite-key effects and intensity fluctuations of the practical photon sources are nonnegligible in a full key rate analysis of practical QKD. In this paper, for the case with finite-key effects and without intensity fluctuations, we present a way to estimate the phase error rate for MDI-QKD and compare performances of the parameter estimation based on Hoeffding’s inequality and the Chernoff bound. By using Azuma’s inequality, we also present the finite-key analysis with composable security against general attacks for a biased decoy-state MDI-QKD protocol with intensity fluctuations. Our simulation results show that the effect of our phase error rate estimation is almost the same as the results in Phys. Rev. A91, 022313 (2015)PLRAAN1050-294710.1103/PhysRevA.91.022313, and the parameter estimation using the Chernoff bound is tighter than that using Hoeffding’s inequality. In addition, the influence of intensity fluctuations is more obvious when the data size of total transmitting signals is small. Our results highlight that it is important to keep the stability of the intensity modulator and estimate accurately the emitted pulse’s intensity for practical implementations.