Quantum key distribution based on heterogeneous air-water channels with foam-covered irregular sea surfaces

For air-water Quantum Key Distribution (QKD), considering the effects of sea breeze, irregular sea surfaces with foam, the complicacy and variety of air-water channels and multiple scattering processes of the polarized quantum state, a heterogeneous air-water channel composite model is established. Based on this, the theoretical model of the error rate of air-water QKD systems is improved. Then, through a polarization vector Monte Carlo simulation, the transmission characteristics of photons in heterogeneous air-water channels and the overall transmission performance of air-water QKDs under different marine environments are analyzed in detail. The results show that heterogeneous air-water channels under clear seawater conditions can achieve a key distribution of 100 meters underwater, but the increase of wind speed and transmission distance will lead to an increase in the photon depolarization ratio and a decrease in fidelity, thereby increasing the polarization error rate. Meanwhile, the rise of wind speed and foam layer thickness adds the quantum error rate of air-water QKD systems and decreases the key generation rate and transmission distance. Both of these factors increase with an increase in signal wavelength. When the wavelength is 532 nm and the channel changes from best(no wind and foam) to worst (storm and foam layer thickness of 6 cm) conditions, the underwater transmission distance is shortened from 120.8 m to 85 m. It can guarantee a 100 m safety depth in underwater vehicles and alternate contingencies such as dragging the buoy can further increase the safety distance of air-water QKD. Therefore, this paper verifies the feasibility of a decoy QKD in a heterogeneous air-water channel with a foam irregular sea surface and acts as a significant reference for future technologies in air-water integrated quantum communication links.