Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Optical Society of America B

Finite-key analysis of practical decoy-state measurement-device-independent quantum key distribution with unstable sources

Yang Wang, Wan‐Su Bao, Chun Hua Zhou, Mu-Sheng Jiang, Hong-Wei Li

Published Feb 1, 2019• 15 citations
Publisher

Abstract

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.

DOI
10.1364/josab.36.000b83

Related papers

Tight finite-key analysis of a practical decoy-state quantum key distribution with unstable sources

Yang Wang, Wan‐Su Bao, Chun Hua Zhou +2 more

The decoy-state quantum key distribution (QKD) protocol has been widely used in commercial QKD systems. Several QKD field networks show its practicability and commercial prospects. Importantly, practical decoy-state QKD systems should be characterized with device imperfections. In this paper, for the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound for a practical decoy-state QKD protocol and compare performances of that based on Hoeffding's inequality and the Chernoff bound, respectively. Taking intensity fluctuations into consideration, we present the finite-key analysis with composable security against general attacks based on Azuma's inequality. Our numerical results show that the finite-key analysis based on the Chernoff bound is tighter than Hoeffding's inequality when the total number of transmitting signals $N<1\ifmmode\times\else\texttimes\fi{}{10}^{12}$. Moreover, the intensity fluctuations' influence is more obvious when the data size of total transmitting signals is small. Our results emphasize the importance of the stability of the intensity modulator as well as the accurate estimation of emitted pulse's intensity.

Physical Review A•Sep 29, 2016•39 citations

Practical passive decoy state measurement-device-independent quantum key distribution with unstable sources

Li Liu, Fen-Zhuo Guo, Qiaoyan Wen

Measurement-device-independent quantum key distribution (MDI-QKD) with the active decoy state method can remove all detector loopholes, and resist the imperfections of sources. But it may lead to side channel attacks and break the security of QKD system. In this paper, we apply the passive decoy state method to the MDI-QKD based on polarization encoding mode. Not only all attacks on detectors can be removed, but also the side channel attacks on sources can be overcome. We get that the MDI-QKD with our passive decoy state method can have a performance comparable to the protocol with the active decoy state method. To fit for the demand of practical application, we discuss intensity fluctuation in the security analysis of MDI-QKD protocol using passive decoy state method, and derive the key generation rate for our protocol with intensity fluctuation. It shows that intensity fluctuation has an adverse effect on the key generation rate which is non-negligible, especially in the case of small data size of total transmitting signals and long distance transmission. We give specific simulations on the relationship between intensity fluctuation and the key generation rate. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account.

Scientific Reports•Sep 6, 2017•6 citations

Improved statistical fluctuation analysis for measurement-device-independent quantum key distribution with four-intensity decoy-state method

Chen-Chen Mao, Xingyu Zhou, Jian-Rong Zhu +3 more

Recently Zhang et al [ Phys. Rev. A95, 012333 (2017)] developed a new approach to estimate the failure probability for the decoy-state BB84 QKD system when taking finite-size key effect into account, which offers security comparable to Chernoff bound, while results in an improved key rate and transmission distance. Based on Zhang et al's work, now we extend this approach to the case of the measurement-device-independent quantum key distribution (MDI-QKD), and for the first time implement it onto the four-intensity decoy-state MDI-QKD system. Moreover, through utilizing joint constraints and collective error-estimation techniques, we can obviously increase the performance of practical MDI-QKD systems compared with either three- or four-intensity decoy-state MDI-QKD using Chernoff bound analysis, and achieve much higher level security compared with those applying Gaussian approximation analysis.

Optics Express•May 8, 2018•25 citations

Biased decoy-state measurement-device-independent quantum key distribution with finite resources

Chun Hua Zhou, Wan‐Su Bao, Hailong Zhang +4 more

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 $(N={10}^{15})$.

arXiv:1505.07284•Physical Review A•Feb 17, 2015•35 citations

Measurement-device-independent quantum key distribution with a passive decoy-state method

Yu-Zhu Shan, Shi‐Hai Sun, Xiang-Chun Ma +3 more

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.

Physical Review A•Oct 28, 2014•19 citations

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

Shi‐Hai Sun, Ming Yuan Gao, Chunyan Li +1 more

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.

arXiv:1305.7396•Physical Review A•May 29, 2013•65 citations
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.
The decoy-state quantum key distribution (QKD) protocol has been widely used in commercial QKD systems. Several QKD field networks show its practicability and commercial prospects. Importantly, practical decoy-state QKD systems should be characterized with device imperfections. In this paper, for the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound for a practical decoy-state QKD protocol and compare performances of that based on Hoeffding's inequality and the Chernoff bound, respectively. Taking intensity fluctuations into consideration, we present the finite-key analysis with composable security against general attacks based on Azuma's inequality. Our numerical results show that the finite-key analysis based on the Chernoff bound is tighter than Hoeffding's inequality when the total number of transmitting signals $N<1\ifmmode\times\else\texttimes\fi{}{10}^{12}$. Moreover, the intensity fluctuations' influence is more obvious when the data size of total transmitting signals is small. Our results emphasize the importance of the stability of the intensity modulator as well as the accurate estimation of emitted pulse's intensity.
Measurement-device-independent quantum key distribution (MDI-QKD) with the active decoy state method can remove all detector loopholes, and resist the imperfections of sources. But it may lead to side channel attacks and break the security of QKD system. In this paper, we apply the passive decoy state method to the MDI-QKD based on polarization encoding mode. Not only all attacks on detectors can be removed, but also the side channel attacks on sources can be overcome. We get that the MDI-QKD with our passive decoy state method can have a performance comparable to the protocol with the active decoy state method. To fit for the demand of practical application, we discuss intensity fluctuation in the security analysis of MDI-QKD protocol using passive decoy state method, and derive the key generation rate for our protocol with intensity fluctuation. It shows that intensity fluctuation has an adverse effect on the key generation rate which is non-negligible, especially in the case of small data size of total transmitting signals and long distance transmission. We give specific simulations on the relationship between intensity fluctuation and the key generation rate. Furthermore, the statistical fluctuation due to the finite length of data is also taken into account.
Recently Zhang et al [ Phys. Rev. A95, 012333 (2017)] developed a new approach to estimate the failure probability for the decoy-state BB84 QKD system when taking finite-size key effect into account, which offers security comparable to Chernoff bound, while results in an improved key rate and transmission distance. Based on Zhang et al's work, now we extend this approach to the case of the measurement-device-independent quantum key distribution (MDI-QKD), and for the first time implement it onto the four-intensity decoy-state MDI-QKD system. Moreover, through utilizing joint constraints and collective error-estimation techniques, we can obviously increase the performance of practical MDI-QKD systems compared with either three- or four-intensity decoy-state MDI-QKD using Chernoff bound analysis, and achieve much higher level security compared with those applying Gaussian approximation 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).
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.