Frequency shifts due to relativistic effects and retardation in continuous-variable quantum key distribution

Space-based quantum communication naturally involves satellites and ground stations exchanging optical signals at high altitudes and large relative velocities. Starting from general relativistic considerations, we systematically separate the frequency shift into longitudinal Doppler contributions, relativistic corrections, and corrections from the propagation delay (retardation). We find the relativistic corrections to the Keplerian satellite orbits to be negligible on the considered timescale, compared to the gravitational and special relativistic time dilation contributions to the frequency shift. Somewhat surprisingly, we find the contribution from the retardation effect to be on the same order of magnitude as the relativistic contributions. To analyze the significance of these effects, we investigate secret key capacities for a continuous variable quantum key distribution protocol for various configurations of satellite orbits and ground stations. We find that the corrections from relativistic effects and retardation significantly impact the communication performance and should be taken into account.