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

Physical Review A

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

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

Published Sep 29, 2016• 39 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.94.032335

Related papers

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

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

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.

Journal of the Optical Society of America B•Feb 1, 2019•15 citations

Finite-key analysis for high-dimensional quantum key distribution with intensity fluctuations

Ya-Hui Gan, Yang Wang, Wan‐Su Bao +3 more

Abstract High-dimensional quantum key distribution (HD-QKD) can increase photon information efficiency and be robust to noise. Several HD-QKD experiments have been demonstrated to verify the above appealing features. However, device imperfections, which have great impacts on the security of HD-QKD system, have not been widely discussed. In this paper, we mainly investigate the finite-key analysis against coherent attacks for HD-QKD without and with intensity fluctuations. For the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound and the improved Chernoff bound. When considering the case with intensity fluctuations, we present the finite-key analysis based on Azuma’s inequality. By numerical simulations, we find that the performance of HD-QKD for the finite-key scenario based on the improved Chernoff bound is tighter than those based on the Chernoff bound or Hoeffding’s inequality in terms of the secret-key rate and the maximum transmission distance. Moreover, we find that intensity fluctuations affect the performance of HD-QKD greatly and the effect for short running time of transmission is more obvious.

Journal of Physics B Atomic Molecular and Optical Physics•Nov 12, 2018•4 citations

Finite-key analysis for a practical decoy-state twin-field quantum key distribution

Shao-Fu He, Yang Wang, Hongwei Li +1 more

Twin-field quantum key distribution (TF-QKD), which is immune to all possible detector side channel attacks, enables two remote legitimate users to perform secure communications without quantum repeaters. With the help of a central node, TF-QKD is expected to overcome the linear key-rate constraint using current technologies. However, the security of the former TF-QKD protocols relies on the hypothesis of infinite-key and stable sources. In this paper, we present the finite-key analysis of a practical decoy-state twin-field quantum key distribution with variant statistical fluctuation models. We examine the composable security of the protocol with intensity fluctuations of unstable sources employing Azuma's inequality. Our simulation results indicate that the secret key rate is able to surpass the linear key-rate bound with limited signal pulses and intensity fluctuations. In addition, the effect of intensity fluctuations is extremely significant for small size of total signals.

arXiv:1910.12416•Oct 28, 2019•0 citations

Finite-key security analysis of decoy-state QKD with source and detector imperfections

Xoel Sixto, Guillermo Currás-Lorenzo, Margarida Pereira +3 more

Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.

quant-pharXiv:2606.29943•Jun 30, 2026•0 citations

Finite-Key Analysis of 1-Decoy Method Quantum Key Distribution with Intensity Fluctuation

Chun Hua Zhou, Yu Zhi Zhou, Yang-Bin Xu +5 more

The decoy state quantum key distribution (QKD) protocol is proven to be an effective strategy against the photon number splitting attack. It was shown that the 1-decoy state protocol, easier to implement in the practical QKD system, outperforms the 2-decoy state protocol for block sizes of up to 108 bits. How intensity fluctuations influence the performance of the 1-decoy state protocol with finite resources remains a pending issue. In this paper, we present a finite-key analysis of the 1-decoy state protocol with intensity fluctuations and obtain the secret key rate formula about intensity fluctuations. Our numerical simulation results show that the stronger the intensity fluctuations, the lower the secret key rate for a small data block size of a few bits. Our research can provide theoretical implications for the selection of data size in the QKD system with intensity fluctuations.

Applied Sciences•May 7, 2022•1 citation

Security of Decoy-State Quantum Key Distribution with Correlated Intensity Fluctuations

Xoel Sixto, Víctor Zapatero, Marcos Curty

One of the most prominent techniques to enhance the performance of practical quantum key distribution (QKD) systems with laser sources is the decoy-state method. Current decoy-state QKD setups operate at gigahertz repetition rates, a regime where memory effects in the modulators and electronics that control them create correlations between the intensities of the emitted pulses. This translates into information leakage about the selected intensities, which cripples a crucial premise of the decoy-state method, thus invalidating the use of standard security analyzes. To overcome this problem, a security proof that exploits the Cauchy-Schwarz constraint has been introduced recently. Its main drawback is, however, that the achievable key rate is significantly lower than that of the ideal scenario without intensity correlations. Here, we improve this security proof technique by combining it with a fine-grained decoy-state analysis, which can deliver a tight estimation of the relevant parameters that determine the secret key rate. This results in a notable performance enhancement, being now the attainable distance double that of previous analyzes for certain parameter regimes. Also, we show that when the probability density function of the intensity fluctuations, conditioned on the current and previous intensity choices, is known, our approach provides a key rate very similar to the ideal scenario, which highlights the importance of an accurate experimental characterization of the correlations.

arXiv:2206.06700•Physical Review Applied•Oct 27, 2022•27 citations
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×\else\texttimes\fi1012N<1\ifmmode\times\else\texttimes\fi{}{10}^{12}N<1\ifmmode×\else\texttimes\fi1012. 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) 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.
Abstract High-dimensional quantum key distribution (HD-QKD) can increase photon information efficiency and be robust to noise. Several HD-QKD experiments have been demonstrated to verify the above appealing features. However, device imperfections, which have great impacts on the security of HD-QKD system, have not been widely discussed. In this paper, we mainly investigate the finite-key analysis against coherent attacks for HD-QKD without and with intensity fluctuations. For the case without intensity fluctuations, we present the parameter estimation based on the Chernoff bound and the improved Chernoff bound. When considering the case with intensity fluctuations, we present the finite-key analysis based on Azuma’s inequality. By numerical simulations, we find that the performance of HD-QKD for the finite-key scenario based on the improved Chernoff bound is tighter than those based on the Chernoff bound or Hoeffding’s inequality in terms of the secret-key rate and the maximum transmission distance. Moreover, we find that intensity fluctuations affect the performance of HD-QKD greatly and the effect for short running time of transmission is more obvious.
Twin-field quantum key distribution (TF-QKD), which is immune to all possible detector side channel attacks, enables two remote legitimate users to perform secure communications without quantum repeaters. With the help of a central node, TF-QKD is expected to overcome the linear key-rate constraint using current technologies. However, the security of the former TF-QKD protocols relies on the hypothesis of infinite-key and stable sources. In this paper, we present the finite-key analysis of a practical decoy-state twin-field quantum key distribution with variant statistical fluctuation models. We examine the composable security of the protocol with intensity fluctuations of unstable sources employing Azuma's inequality. Our simulation results indicate that the secret key rate is able to surpass the linear key-rate bound with limited signal pulses and intensity fluctuations. In addition, the effect of intensity fluctuations is extremely significant for small size of total signals.
Decoy-state quantum key distribution (QKD) is the most widely adopted approach for overcoming the limitations of imperfect single-photon sources. However, existing security proofs typically either neglect important device imperfections or rely on assumptions that are difficult to justify in realistic high-speed implementations, such as the independent and identically distributed nature of the emitted signals. In this work, we combine and extend several recent theoretical advances to provide a comprehensive analytical finite-key security proof for decoy-state QKD that simultaneously incorporates multiple practically relevant transmitter and receiver imperfections, including state-preparation flaws, bit and basis side-channel leakage and correlations, setting-independent intensity fluctuations, and detection-efficiency mismatches.
The decoy state quantum key distribution (QKD) protocol is proven to be an effective strategy against the photon number splitting attack. It was shown that the 1-decoy state protocol, easier to implement in the practical QKD system, outperforms the 2-decoy state protocol for block sizes of up to 108 bits. How intensity fluctuations influence the performance of the 1-decoy state protocol with finite resources remains a pending issue. In this paper, we present a finite-key analysis of the 1-decoy state protocol with intensity fluctuations and obtain the secret key rate formula about intensity fluctuations. Our numerical simulation results show that the stronger the intensity fluctuations, the lower the secret key rate for a small data block size of a few bits. Our research can provide theoretical implications for the selection of data size in the QKD system with intensity fluctuations.
One of the most prominent techniques to enhance the performance of practical quantum key distribution (QKD) systems with laser sources is the decoy-state method. Current decoy-state QKD setups operate at gigahertz repetition rates, a regime where memory effects in the modulators and electronics that control them create correlations between the intensities of the emitted pulses. This translates into information leakage about the selected intensities, which cripples a crucial premise of the decoy-state method, thus invalidating the use of standard security analyzes. To overcome this problem, a security proof that exploits the Cauchy-Schwarz constraint has been introduced recently. Its main drawback is, however, that the achievable key rate is significantly lower than that of the ideal scenario without intensity correlations. Here, we improve this security proof technique by combining it with a fine-grained decoy-state analysis, which can deliver a tight estimation of the relevant parameters that determine the secret key rate. This results in a notable performance enhancement, being now the attainable distance double that of previous analyzes for certain parameter regimes. Also, we show that when the probability density function of the intensity fluctuations, conditioned on the current and previous intensity choices, is known, our approach provides a key rate very similar to the ideal scenario, which highlights the importance of an accurate experimental characterization of the correlations.