Finite-size secret key rate analysis of a discrete-modulated continuous-variable quantum key distribution protocol for satellite-to-ground fading channel

Abstract

Quantum key distribution via satellite-to-ground communication (SatQKD) holds great promise to enable long-distance quantum secure communication. However, SatQKD systems face significant challenges due to satellite orbital movement, atmospheric losses, fading channel and excess noise. Given these challenges, in this work, we investigate the feasibility of the discrete-modulated continuous-variable QKD (DM-CVQKD) protocol using weak coherent pulses and homodyne detection against collective Gaussian attacks for the low Earth orbit SatQKD applications. We evaluate the atmospheric loss model with respect to the satellite overpass geometry and channel fading effects to determine realistic channel parameters such as transmissivity and excess noise. With these channel parameters, we present the asymptotic secret key rate (ASKR) and finite-size secret key rate (FSKR) analysis and identify operational boundaries across different turbulence regimes in terms of satellite elevation angle, the channel transmissivity and excess noise due to various losses along with the suitable time of execution of the protocol. In particular, at weak turbulence with Rytov variance ${\sigma }_R^2=0.1$, we identify the maximum permissible loss as 9.17 dB and the suitable time of execution of the protocol as 461s per satellite pass. Additionally, we compare the FSKR of the DM-CVQKD protocol with the ASKR of the Gaussian-CVQKD protocol and demonstrate the superior performance of the DM-CVQKD protocol at all turbulence strengths. The results underscore the potential of DM-CVQKD protocol as a robust and practical solution for secure satellite-based quantum key distribution.