Security Analysis of MDI-QKD in Turbulent Free-Space Polarization Channels—A Composite Channel Framework

Atmospheric turbulence poses a significant challenge to free-space measurement-device-independent quantum key distribution (FSO MDI-QKD) by inducing polarization decoherence and depolarization, which degrade the secret key rate (SKR). In this paper, we propose a unified depolarizing-dephasing channel model for turbulence-induced polarization decoherence in FSO MDI-QKD. This model consolidates phase perturbations, Gaussian beam spreading, beam drift, aperture truncation, and scintillation into closed-form parameters: depolarization factor, decoherence factor, and detection probability. By mapping turbulence to a von Mises-Fisher/Watson-distributed SU(2) rotation, we derive an analytic SKR expression compatible with existing MDI-QKD security analyses. The model excels in clear, overcast, and hazy weather conditions, offering computational efficiency and experimental verifiability for real-time link adaptation. Numerical simulations, illustrated on a ground-to-satellite free-space link, confirm its accuracy, enabling robust physical layer design for global-scale MDI-QKD networks.