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

arXiv:2304.03562 · EPJ Quantum Technology

Secret key rate bounds for quantum key distribution with faulty active phase randomization

Xoel Sixto, Guillermo Currás-Lorenzo, Kiyoshi Tamaki, Marcos Curty

Published Dec 1, 2023• 12 citations
arXivHTMLPDF

Abstract

Abstract Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires, however, that the phase of each emitted pulse is uniformly random. This might be difficult to guarantee in practice, due to inevitable device imperfections and/or the use of an external phase modulator for phase randomization in an active setup, which limits the possible selected phases to a finite set. Here, we investigate the security of decoy-state QKD when the phase is actively randomized by faulty devices, and show that this technique is quite robust to deviations from the ideal uniformly random scenario. For this, we combine a novel parameter estimation technique based on semi-definite programming, with the use of basis mismatched events, to tightly estimate the parameters that determine the achievable secret key rate. In doing so, we demonstrate that our analysis can significantly outperform previous results that address more restricted scenarios.

DOI
10.1140/epjqt/s40507-023-00210-0

Related papers

Security of quantum key distribution with imperfect phase randomisation

Guillermo Currás-Lorenzo, Shlok Nahar, Norbert Lütkenhaus +2 more

Abstract The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD.

arXiv:2210.08183•Quantum Science and Technology•Dec 11, 2023•28 citations

Imperfect phase randomization and generalized decoy-state quantum key distribution

Shlok Nahar, Twesh Upadhyaya, Norbert Lütkenhaus

Decoy-state methods are essential to perform quantum key distribution (QKD) at large distances in the absence of single-photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed. Moreover, they require that the laser pulses are fully phase randomized. However, realistic high-speed QKD setups do not meet these stringent requirements. In this work, we generalize decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomized states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [G. Curr\'as-Lorenzo, S. Nahar, N. L\"utkenhaus, K. Tamaki, and M. Curty, Quantum Sci. Technol. (2023)] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase randomization on key rates by computing the key rates for a simple implementation of the three-state protocol.

arXiv:2304.09401•Physical Review Applied•Dec 18, 2023•20 citations

Security of quantum key distribution with intensity correlations

Víctor Zapatero, Álvaro Navarrete, Kiyoshi Tamaki +1 more

The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.

arXiv:2105.11165•Quantum•Dec 7, 2021•44 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

Robust quantum key distribution with imperfections in state preparation and characterization

Yi-Fei Lu, Yan-Yang Zhou, Yang Wang +9 more

Quantum key distribution (QKD) offers an approach for secure communication over quantum channels, based on the principles of quantum mechanics. However, the inevitable imperfections in QKD systems can introduce critical vulnerabilities, posing significant challenges to the deployment of QKD in terms of both practical security and performance. In this work, we present a comprehensive security analysis of QKD in the practical scenarios involving imperfections in modulation spaces. Specifically, our analysis focuses on the imperfections related to encoding, intensity modulation, and their characterization. We provide a unified framework based on the operator dominance method to overcome these issues and achieve a tight estimation of the secret key rate (SKR). The simulation results show that the SKR in practical scenarios, with parameters characterized from commercial QKD systems, closely matches the SKR under ideal conditions. In the finite case, the maximum transmission distance can reach up to 250 km with total pulse number $N=10^{12}$ and the SKR closely approaches the asymptotic limit up to 250 km with $N=10^{14}$. This validates the robustness of our method against imperfections in state preparation and characterization. Furthermore, the feasibility and robustness of method in measurement-device-independent (MDI) QKD have also been demonstrated. Our analysis not only promotes advancements in enhancing practical security and performance but also highlights the feasibility of deploying QKD for actual applications.

quant-pharXiv:2610.11438•Physical Review A•Oct 9, 2026•0 citations

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
Abstract Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires, however, that the phase of each emitted pulse is uniformly random. This might be difficult to guarantee in practice, due to inevitable device imperfections and/or the use of an external phase modulator for phase randomization in an active setup, which limits the possible selected phases to a finite set. Here, we investigate the security of decoy-state QKD when the phase is actively randomized by faulty devices, and show that this technique is quite robust to deviations from the ideal uniformly random scenario. For this, we combine a novel parameter estimation technique based on semi-definite programming, with the use of basis mismatched events, to tightly estimate the parameters that determine the achievable secret key rate. In doing so, we demonstrate that our analysis can significantly outperform previous results that address more restricted scenarios.
Abstract The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD.
Decoy-state methods are essential to perform quantum key distribution (QKD) at large distances in the absence of single-photon sources. However, the standard techniques apply only if laser pulses are used that are independent and identically distributed. Moreover, they require that the laser pulses are fully phase randomized. However, realistic high-speed QKD setups do not meet these stringent requirements. In this work, we generalize decoy-state analysis to accommodate laser sources that emit imperfectly phase-randomized states. We also develop theoretical tools to prove the security of protocols with lasers that emit pulses that are independent, but not identically distributed. These tools can be used with recent work [G. Curr\'as-Lorenzo, S. Nahar, N. L\"utkenhaus, K. Tamaki, and M. Curty, Quantum Sci. Technol. (2023)] to prove the security of laser sources with correlated phase distributions as well. We quantitatively demonstrate the effect of imperfect phase randomization on key rates by computing the key rates for a simple implementation of the three-state protocol.
The decoy-state method in quantum key distribution (QKD) is a popular technique to approximately achieve the performance of ideal single-photon sources by means of simpler and practical laser sources. In high-speed decoy-state QKD systems, however, intensity correlations between succeeding pulses leak information about the users' intensity settings, thus invalidating a key assumption of this approach. Here, we solve this pressing problem by developing a general technique to incorporate arbitrary intensity correlations to the security analysis of decoy-state QKD. This technique only requires to experimentally quantify two main parameters: the correlation range and the maximum relative deviation between the selected and the actually emitted intensities. As a side contribution, we provide a non-standard derivation of the asymptotic secret key rate formula from the non-asymptotic one, in so revealing a necessary condition for the significance of the former.
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.
Quantum key distribution (QKD) offers an approach for secure communication over quantum channels, based on the principles of quantum mechanics. However, the inevitable imperfections in QKD systems can introduce critical vulnerabilities, posing significant challenges to the deployment of QKD in terms of both practical security and performance. In this work, we present a comprehensive security analysis of QKD in the practical scenarios involving imperfections in modulation spaces. Specifically, our analysis focuses on the imperfections related to encoding, intensity modulation, and their characterization. We provide a unified framework based on the operator dominance method to overcome these issues and achieve a tight estimation of the secret key rate (SKR). The simulation results show that the SKR in practical scenarios, with parameters characterized from commercial QKD systems, closely matches the SKR under ideal conditions. In the finite case, the maximum transmission distance can reach up to 250 km with total pulse number N=1012N=10^{12}N=1012 and the SKR closely approaches the asymptotic limit up to 250 km with N=1014N=10^{14}N=1014. This validates the robustness of our method against imperfections in state preparation and characterization. Furthermore, the feasibility and robustness of method in measurement-device-independent (MDI) QKD have also been demonstrated. Our analysis not only promotes advancements in enhancing practical security and performance but also highlights the feasibility of deploying QKD for actual applications.
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.