Kalman filter-enabled parameter estimation for simultaneous quantum key distribution and classical communication scheme over a satellite-mediated link.

An accurate estimation of system parameters is of significance for the practical implementation of the simultaneous quantum key distribution and classical communication (SQCC) over a satellite-mediated link when considering the finite-size effect. In this paper, we propose a Kalman filter (KF)-enabled parameter estimation method for the SQCC over a satellite-mediated link. The fast and slow phase drift can be both estimated by using the improved vector KF carrier phase estimation algorithm, and thus the phase estimation error can be tracked in real time and be almost approximate to the theoretical mean square error limit. Taking advantage of the achieved phase estimation and the dual modulation of the SQCC scheme, the excess noise can be estimated with not only a higher precise but also a lower sacrificing rate of raw keys. Numerical simulations demonstrate the feasibility of the SQCC in both the downlink and uplink in terms of the finite-size effect. As a comparison of the Mth-power algorithm, we find that the secret key rate and achievable zenith angle perform better by using the vector KF algorithm. It paves the way of practical implementations for the SQCC system.