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:1002.4083

Continuous-variable Quantum Key Distribution protocols with a discrete modulation

Anthony Leverrier, Philippe Grangier

Published Feb 22, 2010• 24 citations
arXivHTMLPDF

Abstract

In this paper, we consider continuous-variable quantum key distribution with a discrete modulation, either binary or quaternary. We establish the security of these protocols against the class of collective attacks that induce a linear quantum channel. In particular, all Gaussian attacks are taken into account, as well as linear attacks which add a non-Gaussian noise. We give lower bounds for the secret key rate using extremality properties of Gaussian states.

DOI
10.48550/arxiv.1002.4083

Related papers

Long distance quantum key distribution with continuous variables

Anthony Leverrier, Philippe Grangier

We present a continuous-variable quantum key distribution protocol combining a continuous but slightly non-Gaussian modulation together with a efficient reverse reconciliation scheme. We establish the security of this protocol against collective attacks which correspond to a linear quantum channel. In particular, all Gaussian attacks are considered in our framework. We show that this protocol outperforms all known practical protocols, even taking into account finite size effects.

arXiv:1005.0328•May 3, 2010•2 citations

Asymptotic security of discrete-modulation protocols for continuous-variable quantum key distribution

Eneet Kaur, Saikat Guha, Mark M. Wilde

We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.

arXiv:1901.10099•Physical Review A•Jan 15, 2021•52 citations

Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation

Anthony Leverrier, Philippe Grangier

In this paper, we consider continuous-variable quantum-key-distribution (QKD) protocols which use non-Gaussian modulations. These specific modulation schemes are compatible with very efficient error-correction procedures, hence allowing the protocols to outperform previous protocols in terms of achievable range. In their simplest implementation, these protocols are secure for any linear quantum channels (hence against Gaussian attacks). We also show how the use of decoy states makes the protocols secure against arbitrary collective attacks, which implies their unconditional security in the asymptotic limit.

arXiv:1101.3008•Physical Review A•Apr 11, 2011•184 citations

Asymptotic security of binary modulated continuous-variable quantum key distribution under collective attacks

Zhao Yi-Bo, Matthias Heid, Johannes Rigas +1 more

We estimate a lower bound to the secret key rate of a binary modulated continuous variable quantum key distribution scheme. We consider the collective attack scenario with quantum channels that impose arbitrary noise on the exchanged signals. The analysis is done in the infinite key limit. Bob performs ideal homodyne measurements on the received states and the two honest parties employ a reverse reconciliation procedure in the classical postprocessing step of the protocol.

arXiv:0807.3751•Physical Review A•Jan 9, 2009•111 citations

Asymptotic security of the four-state continuous-variable quantum key distribution protocol

Shouvik Ghorai, Philippe Grangier, Eleni Diamanti +1 more

We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution.

•Feb 4, 2019•0 citations

Continuous-variable quantum cryptography with discrete alphabets: Composable security under collective Gaussian attacks

Panagiotis Papanastasiou, Stefano Pirandola

We consider continuous-variable quantum key distribution with discrete-alphabet encodings.In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states.In this setting, we study the composable security in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks.Under this assumption, we can efficiently estimate the parameters of the channel via maximum likelihood estimators and bound the corresponding error in the final secret key rate.

arXiv:1912.11418•Physical Review Research•Jan 14, 2021•53 citations
In this paper, we consider continuous-variable quantum key distribution with a discrete modulation, either binary or quaternary. We establish the security of these protocols against the class of collective attacks that induce a linear quantum channel. In particular, all Gaussian attacks are taken into account, as well as linear attacks which add a non-Gaussian noise. We give lower bounds for the secret key rate using extremality properties of Gaussian states.
We consider discrete-modulation protocols for continuous-variable quantum key distribution (CV-QKD) that employ a modulation constellation consisting of a finite number of coherent states and that use a homodyne- or a heterodyne-detection receiver. We establish a security proof for collective attacks in the asymptotic regime, and we provide a formula for an achievable secret-key rate. Previous works established security proofs for discrete-modulation CV-QKD protocols that use two or three coherent states. The main constituents of our approach include approximating a complex, isotropic Gaussian probability distribution by a finite-size Gauss-Hermite constellation, applying entropic continuity bounds, and leveraging previous security proofs for Gaussian-modulation protocols. As an application of our method, we calculate secret-key rates achievable over a lossy thermal bosonic channel. We show that the rates for discrete-modulation protocols approach the rates achieved by a Gaussian-modulation protocol as the constellation size is increased. For pure-loss channels, our results indicate that in the high-loss regime and for sufficiently large constellation size, the achievable key rates scale optimally, i.e., proportional to the channel's transmissivity.
In this paper, we consider continuous-variable quantum-key-distribution (QKD) protocols which use non-Gaussian modulations. These specific modulation schemes are compatible with very efficient error-correction procedures, hence allowing the protocols to outperform previous protocols in terms of achievable range. In their simplest implementation, these protocols are secure for any linear quantum channels (hence against Gaussian attacks). We also show how the use of decoy states makes the protocols secure against arbitrary collective attacks, which implies their unconditional security in the asymptotic limit.
We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature phase-shift keying (QPSK) modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature amplitude modulations (QAM) schemes. This work is a major step towards establishing the full security of continuous-variable protocols with a discrete modulation in the finite-size regime and opens the way to large-scale deployment of these protocols for quantum key distribution.
We consider continuous-variable quantum key distribution with discrete-alphabet encodings.In particular, we study protocols where information is encoded in the phase of displaced coherent (or thermal) states, even though the results can be directly extended to any protocol based on finite constellations of displaced Gaussian states.In this setting, we study the composable security in the finite-size regime assuming the realistic but restrictive hypothesis of collective Gaussian attacks.Under this assumption, we can efficiently estimate the parameters of the channel via maximum likelihood estimators and bound the corresponding error in the final secret key rate.