Free-space Continuous-variable Quantum Secret Sharing

Free-space quantum cryptography has the potential to enable global quantum communication. However, most existing continuous-variable quantum secret sharing (CV-QSS) schemes rely on fiber channels. In this paper, we present a CV-QSS protocol designed for free-space transmission and construct models of crucial parameters, including channel transmittance, excess noise, and interruption probability, thus deriving the bound of the secret key rate. In particular, we provide a multi-source excess noise model for free-space CV-QSS based on the local local oscillator (LLO) scheme and a straightforward optimization of the noise. Furthermore, our research considers the impact of atmospheric turbulence on the protocol. Simulation results demonstrate that the intensification of atmospheric turbulence adversely affects the aforementioned crucial parameters, leading to a significant reduction in the key rate. However, our protocol shows its capability to securely share secrets over a distance of exceeding $60$ km among five participants in the presence of turbulence with $C^2_n=1\times 10^{-15}m^{-2/3}$, while maintaining a high key rate of approximately $0.55$ bit/pulse over a distance of $10$ km across twenty participants. These findings suggest that efficient CV-QSS in free space is indeed achievable. This research may serve as a reference for the design and optimization of the practical CV-QSS system.