# Performance Analysis of the Shore-to-Reef Atmospheric Continuous-Variable Quantum Key Distribution
## 1 Introduction  
Quantum communication has witnessed rapid development. Quantum key distribution (QKD) [1; 2] is no longer applicable to minor scales and short distances with favorable ambient conditions. Traditional optical fiber channel QKD [3; 4] has not yet met the growing demand, hence atmospheric channel QKD [5; 6; 7] has attracted increasing attention. Compared to optical fiber channel QKD with fixed-attenuation, atmospheric channel QKD could cover a wider range of transmission with more flexible transmission [8; 9]. For example, it is difficult to apply optical fiber channels for quantum communication on the sea, so atmospheric channels have come into play. However, the environments of atmosphere are relatively complicated, and beam propagation in the atmosphere is inevitably affected by the atmosphere [10; 11; 12]. The influence of complex atmosphere on beam propagation mainly involves absorption and scattering of beam by atmospheric molecules and aerosols and disturbance of beam by atmospheric turbulent motion. The former mainly leads to the loss of beam energy, with the name of atmospheric attenuation. The latter causes beam wandering deformation and scintillation [13; 14], commonly referred to as atmospheric turbulence effect. The influence of complex atmosphere on QKD protocol performance cannot be elided. There is some research on it. For example, satellite-sea surface-receiver plane model, underwater QKD model, and air-to-water channel model [15; 16; 17; 18] were proposed for QKD protocol in the sea area. However, there is no complete study on the effect of sea salt on atmospheric continuous-variable quantum key distribution (CVQKD). In fact, compared with metropolitan atmospheric channel, the sea salt contentof the ocean atmospheric channel increases, which has a remarkable effect on the beam transmission and further affects the performance of the protocol. Therefore, for future experiments and applications, it is of great necessity to analyze the effects of sea salt particles on atmospheric CVQKD. The purpose of this paper is to obtain a model of shore-to-reef atmospheric channel CVQKD via exploring the atmospheric attenuation caused by suspended sea salt particles. It is momentous to study the effect of sea salt on the performance of atmospheric channel CVQKD, which ensures the normal implementation of the protocol in high concentration of sea salt atmospheric environment. The extinction effect caused by absorption and scattering of beam by sea salt particles is the main factor affecting the quantum transmission with the large concentration of sea salt. Therefore, based on the characteristics of sea salt particles and Mie scattering theory [19; 20], this paper establishes a sea salt aerosol model and explores the relationship between the extinction factor and the radius of sea salt particles. The results reveal that the extinction factor increases with the growth of the radius of sea salt particles. Then, the study applies the model to the atmospheric channel CVQKD model. Two cases of fixed shore-based distance or sea surface distance is simulated and analyzed, respectively. We find that the secret key rate lessens with the increase of the particle radius, regardless of fixed shore-based distance or fixed sea surface distance. The increase of relative humidity will lead to the decline of secret key rate but the decrease is less than that of particle radius. The research hopes to provide theoretical basis and evaluation support for the implementation of atmospheric channel CVQKD protocol in high concentration of sea salt environment. This paper is organized as follows. In Section 2, ocean atmospheric CVQKD model is established. In Section 3, we describe the atmospheric turbulence effect. In Section 4, a sea salt aerosol model is established to illustrate the extinction effect of sea salt particles on the grounds of characteristics of sea salt particles and Mie scattering theory. In Section 5, the performance of the CVQKD protocol is simulated and analyzed. Finally, conclusions are given in Section 6.