Security of Quantum Key Distribution with Passive Basis Choice and Detection Efficiency Mismatch for a Realistic Satellite Setup

Detection efficiency mismatch is a common problem in realistic quantum key distribution (QKD) systems. Existing security proofs for passive basis choice provide a nonzero secret key rate for small detection efficiency mismatches only. Unfortunately, in realistic setups, the detection efficiency mismatch can be significant. Here, we present a different approach for estimating the secret key rate for the BB84 protocol with passive basis choice and a detection efficiency mismatch between four threshold detectors, where the mismatch is not assumed to be small. We also adapt the decoy-state method for this case. The suggested approach is used to estimate the secret key rate in a QKD experiment between the Micius satellite and the Zvenigorod ground station.