# Performance Analysis of the Shore-to-Reef Atmospheric Continuous-Variable Quantum Key Distribution
## 5 Performance Analysis  
In this section, we analyze the performance of CVQKD protocol based on the previous research of atmospheric sea salt particles aerosol model. We apply Matlab simulations to estimate performance. According to the practical application, the assumption is that one party is on the shore and the other is on the reef when the key is transferred between the two parties. Here we only consider the attenuation caused by sea salt aerosol; conveniently, the attenuation caused by other particles is considered as fixed value. Moreover, excess noise \(\varepsilon=0.03\) in SNU, \(\lambda=550\) nm. In addition, we set \(\beta_{1}=0.9\), \(\eta=0.6\), simply. First, we analyze the effects on secret key rate of sea salt radius and relative humidity under the scenario that the distance between shore-based and sea surface is invariable. The panel in Figure 5a plots the relationship between relative humidity and secret key rate, with the radius of sea salt particles being constant \(r=0.5\)\(\upmu\)m. Figure 5c depicts the relationship between the radius of sea salt particles and the secret key rate when the relative humidity is 80%. Secret key rate as a function of particle radius and relative humidity is illustrated in Figure 5e, where the distance of sea surface is 1 km, 2 km, 3 km, 5 km, 8 km, and 10 km, respectively. As we can notice from the figures, when the distance between shore-based and sea surface remains unchanged, the larger the ocean transmission distances, the smaller the secret key rate. Furthermore, the secret key rate decreases with the increase of the radius of sea salt particles. Compared to the distance of ocean transmission with 1 km, 2 km, 3 km, and 5 km, when the distance of ocean transmission is 8 km and 10 km, the secret key rate decreases to 0 earlier with the increase of particle radius. In addition, the secret key rate lessens with the increase of  
Figure 4: The relationship between particle radius and extinction coefficient. The transmission distance of sea surface is 10 km and the relative humidity is 80%. relative humidity because of the fact that the sea salt particles are hygroscopic particles. The change of relative humidity will cause the variation of particle radius, ultimately contributing to the decrease of the secret key rate. Nevertheless, the decrease in secret key rate is not as dramatic as that caused by particle radius. Second, we analyze the effects on secret key rate of sea salt radius and relative humidity under the scenario that the distance between reef and sea surface is invariable. In Figure 5b, the secret key rate as a function of relative humidity is plotted, when the distance of sea surface is fixed and the sea salt radius is 0.5 \(\upmu\)m. The panel in Figure 5d shows the relationship between secret key rate and sea salt radius. Figure 5: **(a)** The relationship between secret key rate and relative humidity, where the distance of shore-based is invariable and the sea salt radius is 0.5 \(\upmu\)m. **(b)** Secret key rate versus relative humidity, where the distance of sea surface is invariable and sea salt radius is 0.5 \(\upmu\)m. **(c)** Secret key rate versus sea salt radius, where the distance of shore-based is invariable and relative humidity is 80%. **(d)** The relationship between secret key rate and sea salt radius, where relative humidity is 80%. **(e)** Behavior of the secret key rate in terms of relative humidity and sea salt radius, when the distance of sea surface is 1 km, 2 km, 3 km, 5 km, 8 km, and 10 km, while the distance of shore-based is invariable. **(f)** Secret key rate as a function of relative humidity and sea salt radius, where the distance of shore-based is 1 km, 2 km, 3 km, 5 km, 8 km, and 10 km, respectively. salt radius; here relative humidity is 80%. Figure 5f depicts the behavior of the secret key rate in terms of relative humidity and sea salt radius.