Security of quantum key distribution with passive basis choice and detection-efficiency mismatch for a realistic satellite setup

Quantum Key Distribution (QKD) is a cornerstone of secure communication, but its practical implementation is often hindered by hardware imperfections. A major challenge in realistic systems, particularly in satellite-to-ground links, is the detection-efficiency mismatch—where different detectors in the receiver exhibit varying sensitivities. Existing security proofs for passive basis choice often yield a zero secret key rate when this mismatch is large, rendering them ineffective for real-world experimental data from setups like the Micius satellite and the Zvenigorod ground station.

The authors develop a new theoretical framework to estimate the secret key rate by incorporating the specific detection-efficiency mismatch of four threshold detectors. By adopting an entanglement-based formulation of the BB84 protocol and integrating the decoy-state method, the researchers derive an analytical solution that accounts for the statistical differences in detector clicks. This approach avoids the computational burden of numerical methods, allowing for faster real-time processing of satellite QKD data.

The study demonstrates that by properly accounting for the asymmetry in detector efficiencies, one can derive a positive secret key rate even in scenarios with significant hardware imbalances. The authors provide three distinct formulas for the key rate, ranging from a highly detailed version that uses specific statistics for each basis to simplified versions that use aggregated data. They validate this framework using parameters from the Micius-Zvenigorod experiment, showing that their model successfully recovers a non-zero key rate where previous models failed.

This research bridges the gap between theoretical security proofs and the messy reality of experimental quantum hardware. By providing an analytical, rather than numerical, path to calculating secret key rates, the authors facilitate more efficient and robust security analysis for satellite-based quantum networks, which are essential for future global quantum communication infrastructures.