Security analysis of satellite-to-ground reference-frame-independent quantum key distribution with beam wandering

The reference-frame-independent (RFI) quantum key distribution (QKD) is suitable for satellite-based links by removing the active alignment on the reference frames. However, how the beam wandering influences the performance of RFI-QKD remains a pending issue in satellite-to-ground links. In this paper, based on the mathematical model for characterizing beam wandering, we present the security analysis for satellite-to-ground RFI-QKD and analytically derive formulas for calculating the secret key rate with beam wandering. Our simulation results show that the performance of RFI-QKD is better than the Bennett-Brassard 1984 (BB84) QKD with beam wandering in asymptotic case. Furthermore, the degree of influences of beam wandering is specifically presented for satellite-to-ground RFI-QKD when statistical fluctuations are taken into account. Our work can provide theoretical support for the realization of RFI-QKD using satellite-to-ground links and have implications for the construction of large-scale satellite-based quantum networks.