Continuous-Variable Quantum Secret Sharing in Fast-Fluctuating Channels

Recently, several continuous-variable quantum secret sharing (CV-QSS) protocols were proposed, while most of them are limited to the fiber channel systems with a relatively stable transmissivity. However, by means of complex channels, the transmissivity fluctuates dramatically in time with a probability distribution, which will lead to a fast-fluctuating attack. Therefore, the security analysis of CV-QSS in fiber channels may not apply to CV-QSS in complex channels. In this article, we study the CV-QSS protocol in the absence of uniform fast-fluctuating channels whose transmissivity changes with respect to a uniform probability distribution. We give a lower bound of secret key rate to provide security analysis against the fast-fluctuating attack for the CV-QSS protocol. In particular, the realistic highly asymmetric beam splitter (HABS) in CV-QSS protocol is investigated in detail here for the first time, and numerical simulation shows that the security bound is overestimated when the HABS is treated as the perfect device.