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:2409.02630

Discrete-modulated continuous-variable quantum key distribution secure against general attacks

Ignatius William Primaatmaja, Wen Yu Kon, Lim, Charles

Published Sep 4, 2024• 1 citation
arXivHTMLPDF

Abstract

In recent years, discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) has gained traction due to its practical advantages: cost-effectiveness, simple state preparation, and compatibility with existing communication technologies. This work presents a security analysis of DM-CV-QKD against general sequential attacks, including finite-size effects. Remarkably, our proof considers attacks that are neither independent nor identical, and makes no assumptions about the Hilbert space dimension of the receiver. To analyse the security, we leverage the recent generalised entropy accumulation theorem and the numerical methods based on quasi-relative entropy. We also develop a novel dimension reduction technique which is compatible with the entropy accumulation framework. While our analysis reveals significant finite-size corrections to the key rate, the protocol might still offer advantages in specific scenarios due to its practical merits. Our work also offers some insights on how future security proofs can improve the security bounds derived in this work.

DOI
10.48550/arxiv.2409.02630

Related papers

Finite-Size Security for Discrete-Modulated Continuous-Variable Quantum Key Distribution Protocols

Florian Kanitschar, Ian George, Jie Lin +2 more

Discrete-modulated (DM) continuous-variable quantum key distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity.While tight security analyses in the asymptotic limit exist, proofs in the finitesize regime are still subject to active research.We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol.We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's -security framework and address the issue of acceptance sets in protocols and their security proof.We want to highlight that our method also allows for nonunique acceptance statistics, which is necessary in practise.Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate.To demonstrate our method, we apply it to a quadrature phase-shift keying protocol for both untrusted, ideal and trusted, nonideal detectors.The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72 km transmission distance.

arXiv:2301.08686•PRX Quantum•Oct 10, 2023•59 citations

Effective discrete-modulated continuous variable QKD under general attacks using dimension reduction

Mariana Navarro, Mateus Araújo, Antonio Acín +1 more

Continuous variable quantum key distribution via discrete modulations ensures information-theoretic security using standard telecom technologies, providing affordable and scalable quantum communications with simplified classical postprocessing. However, existing security proofs against general attacks often rely on restrictive assumptions, such as a bounded dimension for coherent states, or require impractically large block sizes. In this work, we develop a finite-size security analysis that removes these limitations while incorporating realistic experimental features. Our approach combines an optimization under infinite dimensions, a security proof against general attacks, a trusted detector model accounting for the receiver imperfections, and postselection strategies to reuse discarded measurement outcomes. We report positive key rates in the finite-size regime for relevant block sizes of the order of $10^7$. These results contribute to narrowing the gap between theoretical security proofs and practical implementations of discrete-modulated continuous variable quantum key distribution protocols.

quant-pharXiv:2606.20346•Jun 19, 2026•0 citations

Unconditional Security of Discrete-Modulated CV-QKD from Infinite-Dimensional MEAT

Lars Kamin, Ian George, John Burniston +1 more

Discrete-Modulated (DM) Continuous-Variable (CV) Quantum Key Distribution (QKD) is an experimentally attractive approach to quantum cryptography, offering high key rates over metropolitan-scale distances while relying on state-of-the-art telecom infrastructure. However, a fundamental gap has remained between this experimental promise and rigorous security: for more than two decades, DM CV-QKD has lacked a complete composable finite-size security proof against coherent attacks. Existing works either restrict the adversary to collective attacks, impose additional finite-dimensional assumptions, apply only to specific modulation formats, or fail to recover the known asymptotic rates. Here, we resolve this longstanding problem by establishing the first complete composable finite-size security proof for DM CV-QKD protocols against coherent attacks, incorporating imperfect detectors and both fixed- and variable-length protocol variants. Our proof introduces two central results of broader interest: an infinite-dimensional marginal-constrained entropy accumulation theorem (iMEAT) and a rigorous dimension-reduction technique that makes the infinite-dimensional security bounds numerically tractable. The resulting key rates recover the known asymptotic rates and outperform established finite-size bounds based on collective attacks, while yielding positive key rates beyond $70$km for experimentally relevant block sizes and parameters. Thus, our work closes a longstanding gap and places an experimentally attractive class of CV-QKD protocols on a rigorous composable security footing and provides a pathway towards their practical deployment.

quant-pharXiv:2609.16105•Sep 16, 2026•0 citations

An introductory review of the theory of continuous-variable quantum key distribution: Fundamentals, protocols, and security

Maron F Anka, John A. Mora Rodríguez, Douglas F. Pinto +3 more

Continuous-variable quantum key distribution (CV-QKD) has emerged as a promising approach for secure quantum communication, offering advantages such as high key generation rates, compatibility with standard telecommunication infrastructure, and potential for integration on photonic chips. This review provides an accessible introduction to the theory of CV-QKD, aimed at researchers entering this rapidly developing field. We focus on fundamental concepts, key protocols, and security analysis essential for understanding CV-QKD systems, with a special emphasis on prepare-and-measure protocols using coherent states under asymptotic security conditions. We explain their equivalence to entanglement-based protocols and detail the security proof framework against collective attacks, encompassing both Gaussian and discrete modulation schemes. We also briefly address more advanced topics, including measurement-device-independent CV-QKD and finite-size security analysis. This work is motivated by Brazil's growing investment in quantum communication technologies. By presenting a clear learning path from basic concepts to advanced topics, this work aims to equip newcomers with the essential tools to engage with current research in CV-QKD, thereby supporting the training of a new generation of researchers in this strategic field.

quant-pharXiv:2512.01758•Brazilian Journal of Physics•Dec 2, 2025•4 citations

Improved finite-size key rates for discrete-modulated continuous-variable quantum key distribution under coherent attacks

Carlos Pascual-García, Stefan Bäuml, Mateus Araújo +2 more

Continuous-variable quantum key distribution (CVQKD) with discrete modulation combines advantages of CVQKD, such as implementability using readily available technologies, with advantages of discrete variable quantum key distribution, such as easier error correction procedures. We consider a prepare-and-measure CVQKD protocol, where Alice chooses from a set of four coherent states and Bob performs a heterodyne measurement, the result of which is discretized in both key and test rounds. We provide a security proof against coherent attacks in the finite-size regime based on the generalized entropy accumulation theorem. We compute the corresponding asymptotic key rate imposing a photon-number cutoff and recent advances in conic optimization. Our method yields significant improvements on key rates: at metropolitan distances, it provides positive key rates for block sizes of the order of ${10}^{8}$ rounds, orders of magnitude smaller compared to previous works.

arXiv:2407.03087•Physical Review A•Feb 11, 2025•14 citations

Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution

Takaya Matsuura, Shinichiro Yamano, Yui Kuramochi +2 more

Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.

arXiv:2301.03171•Quantum•Aug 29, 2023•9 citations
In recent years, discrete-modulated continuous-variable quantum key distribution (DM-CV-QKD) has gained traction due to its practical advantages: cost-effectiveness, simple state preparation, and compatibility with existing communication technologies. This work presents a security analysis of DM-CV-QKD against general sequential attacks, including finite-size effects. Remarkably, our proof considers attacks that are neither independent nor identical, and makes no assumptions about the Hilbert space dimension of the receiver. To analyse the security, we leverage the recent generalised entropy accumulation theorem and the numerical methods based on quasi-relative entropy. We also develop a novel dimension reduction technique which is compatible with the entropy accumulation framework. While our analysis reveals significant finite-size corrections to the key rate, the protocol might still offer advantages in specific scenarios due to its practical merits. Our work also offers some insights on how future security proofs can improve the security bounds derived in this work.
Discrete-modulated (DM) continuous-variable quantum key distribution (CV-QKD) protocols are promising candidates for commercial implementations of quantum communication networks due to their experimental simplicity.While tight security analyses in the asymptotic limit exist, proofs in the finitesize regime are still subject to active research.We present a composable finite-size security proof against independently and identically distributed collective attacks for a general DM CV-QKD protocol.We introduce a new energy testing theorem to bound the effective dimension of Bob's system and rigorously prove security within Renner's -security framework and address the issue of acceptance sets in protocols and their security proof.We want to highlight that our method also allows for nonunique acceptance statistics, which is necessary in practise.Finally, we extend and apply a numerical security proof technique to calculate tight lower bounds on the secure key rate.To demonstrate our method, we apply it to a quadrature phase-shift keying protocol for both untrusted, ideal and trusted, nonideal detectors.The results show that our security proof method yields secure finite-size key rates under experimentally viable conditions up to at least 72 km transmission distance.
Continuous variable quantum key distribution via discrete modulations ensures information-theoretic security using standard telecom technologies, providing affordable and scalable quantum communications with simplified classical postprocessing. However, existing security proofs against general attacks often rely on restrictive assumptions, such as a bounded dimension for coherent states, or require impractically large block sizes. In this work, we develop a finite-size security analysis that removes these limitations while incorporating realistic experimental features. Our approach combines an optimization under infinite dimensions, a security proof against general attacks, a trusted detector model accounting for the receiver imperfections, and postselection strategies to reuse discarded measurement outcomes. We report positive key rates in the finite-size regime for relevant block sizes of the order of 10710^7107. These results contribute to narrowing the gap between theoretical security proofs and practical implementations of discrete-modulated continuous variable quantum key distribution protocols.
Discrete-Modulated (DM) Continuous-Variable (CV) Quantum Key Distribution (QKD) is an experimentally attractive approach to quantum cryptography, offering high key rates over metropolitan-scale distances while relying on state-of-the-art telecom infrastructure. However, a fundamental gap has remained between this experimental promise and rigorous security: for more than two decades, DM CV-QKD has lacked a complete composable finite-size security proof against coherent attacks. Existing works either restrict the adversary to collective attacks, impose additional finite-dimensional assumptions, apply only to specific modulation formats, or fail to recover the known asymptotic rates. Here, we resolve this longstanding problem by establishing the first complete composable finite-size security proof for DM CV-QKD protocols against coherent attacks, incorporating imperfect detectors and both fixed- and variable-length protocol variants. Our proof introduces two central results of broader interest: an infinite-dimensional marginal-constrained entropy accumulation theorem (iMEAT) and a rigorous dimension-reduction technique that makes the infinite-dimensional security bounds numerically tractable. The resulting key rates recover the known asymptotic rates and outperform established finite-size bounds based on collective attacks, while yielding positive key rates beyond 707070km for experimentally relevant block sizes and parameters. Thus, our work closes a longstanding gap and places an experimentally attractive class of CV-QKD protocols on a rigorous composable security footing and provides a pathway towards their practical deployment.
Continuous-variable quantum key distribution (CV-QKD) has emerged as a promising approach for secure quantum communication, offering advantages such as high key generation rates, compatibility with standard telecommunication infrastructure, and potential for integration on photonic chips. This review provides an accessible introduction to the theory of CV-QKD, aimed at researchers entering this rapidly developing field. We focus on fundamental concepts, key protocols, and security analysis essential for understanding CV-QKD systems, with a special emphasis on prepare-and-measure protocols using coherent states under asymptotic security conditions. We explain their equivalence to entanglement-based protocols and detail the security proof framework against collective attacks, encompassing both Gaussian and discrete modulation schemes. We also briefly address more advanced topics, including measurement-device-independent CV-QKD and finite-size security analysis. This work is motivated by Brazil's growing investment in quantum communication technologies. By presenting a clear learning path from basic concepts to advanced topics, this work aims to equip newcomers with the essential tools to engage with current research in CV-QKD, thereby supporting the training of a new generation of researchers in this strategic field.
Continuous-variable quantum key distribution (CVQKD) with discrete modulation combines advantages of CVQKD, such as implementability using readily available technologies, with advantages of discrete variable quantum key distribution, such as easier error correction procedures. We consider a prepare-and-measure CVQKD protocol, where Alice chooses from a set of four coherent states and Bob performs a heterodyne measurement, the result of which is discretized in both key and test rounds. We provide a security proof against coherent attacks in the finite-size regime based on the generalized entropy accumulation theorem. We compute the corresponding asymptotic key rate imposing a photon-number cutoff and recent advances in conic optimization. Our method yields significant improvements on key rates: at metropolitan distances, it provides positive key rates for block sizes of the order of 108{10}^{8}108 rounds, orders of magnitude smaller compared to previous works.
Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.