2019/01/31 by Eneet Kaur, Saikat Guha, Mark M. Wilde
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Computer science #Cryptography #Gaussian #Information-theoretic security #Mathematics #Modulation (music) #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum key distribution #Quantum mechanics #Theoretical computer science #Topology (electrical circuits) #quant-ph
paper · pdf · doi:10.1103/physreva.103.012412
published as Phys. Rev. A 103, 012412 (2021) · 25 pages, 4 figures
openalex publication_date 2021/01/15 · arxiv created 2021/01/19 · arxiv updated 2021/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.