Security analysis of free-space discrete modulated continuous-variable quantum key distribution with precise channel characterization and postselection strategies
Phys. Rev. Applied 25, 024013 – Published 4 February, 2026
DOI: https://doi.org/10.1103/v7d9-ylyl
Abstract
Free-space continuous-variable quantum key distribution (CV-QKD) is attractive for its low cost, operational simplicity, and deployment flexibility. Discrete modulation further enhances practicality, yet rigorous security analysis over free-space channels is challenging because turbulence-induced fluctuations are compounded by the non-Gaussian nature of discrete modulation. We perform a fully numerical characterization of the free-space quantum channel, avoiding the simplifying assumptions inherent in existing analytical models. Together with a semidefinite-programming method, we establish an asymptotic security analysis framework of free-space discrete modulated (DM) CV-QKD without invoking Gaussian optimality. Unlike the cutoff behavior implied by the analytical models of transmittance probability distribution, our numerical results exhibit a pronounced long tail, indicating that the models assign larger probability mass to low transmittance and might overestimate turbulence-driven fluctuations. Based on the precise channel characterization, we compute tight lower bounds on the asymptotic secret key rate (SKR) under weak and moderate turbulence, and systematically assess postselection strategies. We find that optimized amplitude postselection increases the SKR, whereas phase postselection consistently degrades it. Additionally, in the absence of finite-size effects, transmittance-based postselection yields further gain.
