# Performance of Ship-Based QKD Under the Influence of Sea-Surface Atmospheric Turbulence
## 3 The Influence of Sea-Surface Turbulence on the Performances of a Ship-Based QKD
### The Satellite-to-Ship QKD System  
In the satellite-to-ship QKD system, the transmitting end is fixed on a ship, and the receiving transmitting end is fixed on a satellite. Figure 4 shows the relationship between photon counts and the zenith angle when the satellite orbit altitude is 400 km. It can be seen that photon counts reach a maximum value at a zenith angle of 12 degrees; when the zenith angle is greater than 30 degrees, the photon count is very small. This is mainly due to the influence of atmospheric attenuation and geometric loss of light, limiting its transmission distance. In other words, the QKD system has a limited communication distance in the same orbital altitude, and the transmission distance varies with the zenith angle. Only the system in which the corresponding zenith angle is within the communication distance limit can be coded. This is why photon counts increase and then decrease as the zenith angle increases. When the zenith angle corresponding to the distance limit is exceeded, it is impossible to code.  
The relationship between secure keys and satellite orbital altitude for different intensities of turbulence is shown in Figure 5. These curves show that under weak turbulence conditions (Cn\({}^{2}\) = 10\({}^{-17}\)), the system can communicate with satellites at an orbital altitude of 619 km; under middle-intensity turbulence conditions (Cn\({}^{2}\) = 10\({}^{-15}\)), the system can communicate with satellites at an orbital altitude of 466 km; and under strong turbulence conditions (Cn\({}^{2}\) = 10\({}^{-13}\)), the system can communicate with satellites at an orbital altitude of 173 km. From these data, it can be seen that the communication distance between the offshore platform and the satellite QKD system decreases with an increase in turbulence intensity due to the influence of sea-surface atmospheric turbulence.  
Figure 4: Photon counts versus zenith angle.  
Based on the above results, the system was optimized to ensure that the transmitting end could communicate with the receiving end on a satellite at an orbital altitude of 1000 km. Figure 5(a) shows the diagram of photons counts received versus satellite orbit altitude when the zenith angle is 15 degrees, Figure 5(b) shows a diagram of quantum BER (QBER) versus satellite orbit altitude for different turbulence intensities. It can be seen that the performances are seriously affected by strong turbulence. In strong turbulence, the photon counts are significantly lower, and the QBER performance significantly increases.  
When the zenith angle is 15 degrees, the curves in Figure 6(a) represent the relationship between photon counts by the system and satellite orbit altitude under different turbulence intensities, and the curves in Figure 6(b) represent the relationship between QBER and satellite orbit altitude under different turbulence intensities. When comparing the data in Figures 6 and 7, it can be seen that under the same turbulence conditions, the photon counts by the system with a zenith angle of 15 degrees are higher than that with a zenith angle of 30 degrees. The performance of QBER under a zenith angle of 15 degrees is better than that under a zenith angle of 30 degrees, too. This is due to the fact that, at the same satellite orbital altitude, the larger the zenith angle, the longer the link distance, the greater the attenuation caused by the atmospheric turbulence, thus affecting photon counts.  
Figure 5: Secure keys versus satellite orbit altitude.  
Figure 6: Photon counts (**a**) and QBER (**b**) versus satellite orbital altitude at a \(30^{\circ}\) zenith angle.