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

Abstract

Atmospheric turbulence poses a significant challenge to free-space measurement-device-independent quantum key distribution (FSO MDI-QKD) by inducing polarization distortions and stochastic propagation losses, which together degrade the secret key rate (SKR). In this paper, we propose a composite channel framework that unifies phase perturbations, beam spreading, beam drift, receiver-aperture truncation, scintillation-induced fading, and atmospheric attenuation into a compact set of closed-form interface parameters: an effective depolarization parameter, an effective decoherence parameter, and an effective end-to-end detection probability. By modeling turbulence-induced polarization changes as random polarization rotations with axis statistics captured by a directional distribution, we obtain a Pauli-diagonal effective depolarizing–dephasing description and derive an analytic SKR evaluation that can be directly embedded into standard MDI-QKD security analysis. We incorporate representative clear, overcast, and hazy profiles through weather-dependent attenuation and turbulence conditions, and the resulting parameterization enables computationally efficient SKR evaluation and link-parameter sweeps. Numerical case studies on a ground-to-satellite free-space link illustrate the SKR trends under the proposed framework, supporting physical-layer design and performance assessment for satellite-based MDI-QKD networks.