Considering the air-water interface and ocean water's optical attenuation, the performance of quantum key distribution (QKD) based on air-water channel is studied. The effects of photons' various incident angles to air-water interface on quantum bit error rate (QBER) and the maximum secure transmission distance are analyzed. Taking the optical attenuation of ocean water into account, the performance bounds of QKD in different types of ocean water are discussed. The simulation results show that the maximum secure transmission distance of QKD gradually reduces as the incident angle from air to ocean water increases. In the clearest ocean water with the lowest attenuation, the maximum secure transmission distance of photons far exceeds the the working depth of underwater vehicles. In intermediate and murky ocean waters with higher attenuation, the secure transmission distance shortens, but the underwater vehicle can deploy other accessorial methods for QKD with perfect security. So the implementation of OKD between the satellite and the underwater vehicle is feasible."Quantum secure communication of China Beijing Shanghai line" project has been started, which proves a great leap of quantum key distribution (QKD) [1] from experiment to application [2] . In recent years, many theoretical and experimental researches have been carried out towards the development of practical QKD systems based on optical fibers [3][4][5][6][7][8][9][10][11][12][13][14] and free-space [15][16][17] . However, people have higher expectations that the quantum secure communication can completely improve the underwater communication. Marco Lanzagorta [18] presented a good idea that QKD can be implemented between the satellite and the underwater vehicle to construct a two-way laser communication link with perfect security, and theoretically proved that the implementation of BB84 QKD protocol between two users submerged in ocean water was feasible. Ref. [19] analyzed the influence of the transmission rates of different photon components on quantum bit error rate (QBER) of QKD between different media. However, other than the influence of air-water interface, there is much challenge confronted by the photon signals from air to ocean water, such as the larger optical attenuation of ocean water, various noise and quantum efficiency of photodetector.In this paper, synthetically considering the influence of the air-water interface and the optical attenuation of the ocean water on QKD, the maximum secure transmission distances of BB84 QKD in different types of water are analyzed, and a more comprehensive demonstration for the feasibility of implementing OKD between the satellite and the underwater vehicle is provided.As shown in Fig.1, there is an incident ray with wave vector k from the medium with refractive index n 1 to the medium with refractive index n 2 , and the angle of refraction is γ.
Fig.1 Schematic diagram of the photons transmitting between different mediaThen we define t p and t s to be the amplitude transmittances of s component and p co...