Security of discrete-modulated continuous-variable quantum key distribution

Abstract

Continuous variable quantum key distribution with discrete modulation has the potential to provide information-theoretic security using widely available optical elements and existing telecom infrastructure. While their implementation is significantly simpler than that for protocols based on Gaussian modulation, proving their finite-size security against coherent attacks poses a challenge. In this work we prove finite-size security against coherent attacks for a discrete-modulated quantum key distribution protocol involving four coherent states and heterodyne detection. To do so, and contrary to most of the existing schemes, we first discretize all the continuous variables generated during the protocol. This allows us to use the entropy accumulation theorem, a tool that has previously been used in the setting of discrete variables, to construct the finite-size security proof. We then compute the corresponding finite-key rates through semi-definite programming and under a photon-number cutoff. Our analysis provides asymptotic rates in the range of $0.1-10^{-4}$ bits per round for distances up to hundred kilometres, while in the finite case and for realistic parameters, we get of the order of $10$ Gbits of secret key after $n\sim 10^{11}$ rounds and distances of few tens of kilometres.

Accepted version

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Cited by in corpus (12)

• Continuous-variable quantum key distribution system: past, present, and future
• Continuous-variable quantum communication
• Experimental composable key distribution using discrete-modulated continuous variable quantum cryptography
• Improved finite-size key rates for discrete-modulated continuous variable quantum key distribution under coherent attacks
• Finite-size analysis of prepare-and-measure and decoy-state QKD via entropy accumulation
• A Survey on Continuous Variable Quantum Key Distribution for Secure Data Transmission: Toward the Future of Secured Quantum-Networks
• An introductory review of the theory of continuous-variable quantum key distribution: Fundamentals, protocols, and security
• Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation
• Continuous-Variable Quantum Key Distribution with Composable Security and Tight Error Correction Bound towards Constrained-Device Implementations
• Finite-size secret-key rates of discrete modulation continuous-variable quantum key distribution under Gaussian attacks
• Finite-size security of QKD: comparison of three proof techniques
• Security proofs for practical QKD: variations, techniques, gaps, and limitations