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

Statistical fluctuation analysis for one-decoy-state quantum key distribution

Lei Chen, Xiao-Ming Chen, Yalong Yan

Published May 3, 2022• 0 citations
Publisher

Abstract

Abstract One-decoy-state quantum key distribution with infinite length pulses can even approach the asymptotic case, i.e., infinite decoy states and infinite length pulses. Due to the limitation of experimental time, we must consider the statistical fluctuation caused by the finite number of pulses. The central limit theorem analysis method is an effective method, which can easily give the upper and lower bounds of experimental observations. Combining the central limit theorem method with the theorem that the ratio of two independent normal random variables can be approximated as a normal random variable under certain conditions, we propose a more efficient method to estimate the secure key rate. Compared with using central limit theorem method directly, our method has fewer bounds, smaller estimation deviation and higher estimation accuracy. The simulation results show that our method can significantly improve the secure key rate and transmission distance when considering statistical fluctuation and keeping the pulse number and security parameters unchanged, especially in the case of small pulse number (e.g. 107).

DOI
10.21203/rs.3.rs-1601520/v1

Related papers

Tight security bounds for decoy-state quantum key distribution

Hua-Lei Yin, Min-Gang Zhou, Jie Gu +3 more

The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and most importantly, the security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is the deviation between phase error rate of computational basis and bit error rate of dual basis. Here, we provide the rigorous and optimal analytic formula to solve the above tasks, resulting to higher secret key rate and longer secure transmission distance. Our results can be widely applied to deal with statistical fluctuation in quantum cryptography protocols.

arXiv:2002.06530•Scientific Reports•Aug 31, 2020•75 citations

Practical issues in decoy-state quantum key distribution based on the central limit theorem

Anton Sergeevich Trushechkin, Evgeniy O. Kiktenko, Aleksey K. Fedorov

Decoy-state quantum key distribution (QKD) is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or ``finite-key effects''). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as inclusion of the failure probability of the decoy-state statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.

arXiv:1702.08531•Physical Review A•Aug 17, 2017•21 citations

An effected process on finite statistical fluctuation analysis for decoy-state measurement device-independent quantum key distribution

Su-Tong Shi, Fen-Zhuo Guo

In this paper, we consider the decoy-state Measurement-Device-Independent Quantum key distribution (MDI-QKD) with four intensities. The average value of successful events and bit errors among the pulse pair set be used to investigate the successful events of different pulses under the statistical fluctuation caused by the finite condition. We demonstrate that the lower bound of successful events number n11estimated by our method can be more tight than the result in [28]. Numerical simulations show that our estimation method can achieve a higher key rate than existing methods with a relatively weak constraints of experimental devices, such as high dark count rate and low detection efficiency of detectors when data size is N = 109.

arXiv:1610.04311•Oct 14, 2016•0 citations

Statistical-fluctuation analysis for quantum key distribution with consideration of after-pulse contributions

Hongxin Li, Haodong Jiang, Ming Gao +3 more

The statistical fluctuation problem is a critical factor in all quantum key distribution (QKD) protocols under finite-key conditions. The current statistical fluctuation analysis is mainly based on independent random samples, however, the precondition cannot always be satisfied because of different choices of samples and actual parameters. As a result, proper statistical fluctuation methods are required to solve this problem. Taking the after-pulse contributions into consideration, this paper gives the expression for the secure key rate and the mathematical model for statistical fluctuations, focusing on a decoy-state QKD protocol [Z.-C. Wei et al., Sci. Rep. 3, 2453 (2013)] with a biased basis choice. On this basis, a classified analysis of statistical fluctuation is represented according to the mutual relationship between random samples. First, for independent identical relations, a deviation comparison is made between the law of large numbers and standard error analysis. Second, a sufficient condition is given that the Chernoff bound achieves a better result than Hoeffding's inequality based on only independent relations. Third, by constructing the proper martingale, a stringent way is proposed to deal issues based on dependent random samples through making use of Azuma's inequality. In numerical optimization, the impact on the secure key rate, the comparison of secure key rates, and the respective deviations under various kinds of statistical fluctuation analyses are depicted.

arXiv:1507.01222•Physical Review A•Dec 30, 2015•13 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

Analysis of decoy-state measurement-device-independent quantum key distribution system

Peng Zhang, Rongzhen Jiao

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.

International Journal of Quantum Information•Feb 1, 2019•0 citations
Abstract One-decoy-state quantum key distribution with infinite length pulses can even approach the asymptotic case, i.e., infinite decoy states and infinite length pulses. Due to the limitation of experimental time, we must consider the statistical fluctuation caused by the finite number of pulses. The central limit theorem analysis method is an effective method, which can easily give the upper and lower bounds of experimental observations. Combining the central limit theorem method with the theorem that the ratio of two independent normal random variables can be approximated as a normal random variable under certain conditions, we propose a more efficient method to estimate the secure key rate. Compared with using central limit theorem method directly, our method has fewer bounds, smaller estimation deviation and higher estimation accuracy. The simulation results show that our method can significantly improve the secure key rate and transmission distance when considering statistical fluctuation and keeping the pulse number and security parameters unchanged, especially in the case of small pulse number (e.g. 107).
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and most importantly, the security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is the deviation between phase error rate of computational basis and bit error rate of dual basis. Here, we provide the rigorous and optimal analytic formula to solve the above tasks, resulting to higher secret key rate and longer secure transmission distance. Our results can be widely applied to deal with statistical fluctuation in quantum cryptography protocols.
Decoy-state quantum key distribution (QKD) is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or ``finite-key effects''). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as inclusion of the failure probability of the decoy-state statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.
In this paper, we consider the decoy-state Measurement-Device-Independent Quantum key distribution (MDI-QKD) with four intensities. The average value of successful events and bit errors among the pulse pair set be used to investigate the successful events of different pulses under the statistical fluctuation caused by the finite condition. We demonstrate that the lower bound of successful events number n11estimated by our method can be more tight than the result in [28]. Numerical simulations show that our estimation method can achieve a higher key rate than existing methods with a relatively weak constraints of experimental devices, such as high dark count rate and low detection efficiency of detectors when data size is N = 109.
The statistical fluctuation problem is a critical factor in all quantum key distribution (QKD) protocols under finite-key conditions. The current statistical fluctuation analysis is mainly based on independent random samples, however, the precondition cannot always be satisfied because of different choices of samples and actual parameters. As a result, proper statistical fluctuation methods are required to solve this problem. Taking the after-pulse contributions into consideration, this paper gives the expression for the secure key rate and the mathematical model for statistical fluctuations, focusing on a decoy-state QKD protocol [Z.-C. Wei et al., Sci. Rep. 3, 2453 (2013)] with a biased basis choice. On this basis, a classified analysis of statistical fluctuation is represented according to the mutual relationship between random samples. First, for independent identical relations, a deviation comparison is made between the law of large numbers and standard error analysis. Second, a sufficient condition is given that the Chernoff bound achieves a better result than Hoeffding's inequality based on only independent relations. Third, by constructing the proper martingale, a stringent way is proposed to deal issues based on dependent random samples through making use of Azuma's inequality. In numerical optimization, the impact on the secure key rate, the comparison of secure key rates, and the respective deviations under various kinds of statistical fluctuation analyses are depicted.
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.
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.