## 3 Secret Key Rate in Inter-Satellite Links
### Simulation and Discussion
For \(d=3000\) km, \(V_{M}=7\) and \(n=5\), the SKR can exceed \(10^{-3}\) bits/pulse. We also plot the relationship between the SKR and \(V_{M}\) with different excess noise \(\xi_{0}\) as shown in Figure 4b. We can see that as the excess noise \(\xi_{0}\) increases, the optimal domains of \(V_{M}\) are constricted. Similarly, there is also a symmetric point located at \(V_{M}=7\). Thus, we can obtain a common optimal \(V_{M}\) as 7. In particular, we find that the SKR can achieve \(2\times 10^{-3}\) bits/pulse for \(d=1500\) km, \(V_{M}=7\), and \(\xi_{0}=0.003\). In view of Figure 5a, we analyze the influence of different reconciliation efficiency and numbers of players on the SKR with \(f=50\) THz and \(V_{M}=7\). We can observe that \(\beta\) is very sensitive to the influence of the maximal transmission distance. For \(n=8\), the maximal transmission distance can reach 3600 km with \(\beta=0.98\) and 2165 km with \(\beta=0.95\). The difference between them is 1435 km. Nevertheless, for \(n=15\), the difference between them is 377 km (the maximal transmission distance is 1525 km for \(\beta=0.98\) and 1148 km for \(\beta=0.95\)). Figure 5b demonstrates the influence of different excess noise and numbers of players on the SKR. It is clear that in the case of the same number of players, \(\xi_{0}\) is also very sensitive to the influence of the maximal transmission distance. For \(n=8\), the maximal transmission distance can achieve 3600 km with \(\xi_{0}=0.001\), 1615 km with \(\xi_{0}=0.002\) and 1146 km with \(\xi_{0}=0.003\). Interestingly, we can see that a \(10^{-5}\) bits/pulse SKR at almost 2300 km can be achieved with \(n=10\), \(\xi=0.001\) and \(\beta=0.98\) from Figure 5. This result shows the powerful performance of our THz-CVQSS system. In short, from the aforementioned analysis, THz-CVQSS can achieve the optimal SKR with higher frequency, the optimal \(V_{M}\) value, higher reconciliation efficiency and lower excess noise in inter-satellite links. Figure 4: (**a**) The relationship between the SKR and the modulation variance \(V_{M}\) with different transmission distance and numbers of players. \(\xi_{0}=0.001,\eta=0.6,v_{d}=0.1,\beta=0.98\), and \(f=50\) THz. (**b**) The relationship between the SKR and the modulation variance \(V_{M}\) with different transmission distance and excess noise. \(n=5,\eta=0.6,v_{d}=0.1,\beta=0.98\), and \(f=50\) THz. Due to the length of the SKR is limited at finite-size of data in the actual CVQSS system, we further consider the finite-size SKR of THz-CVQSS as shown in Figure 6. The detailed analysis of finite-size SKR is provided in Appendix A. We can observe that the maximal transmission distance increases with the increase of \(M\) and gradually approaches the case of SKR-unlimited. For \(M=10^{14}\) and \(n=5\), the maximal transmission distance can attain about \(2300\) km with \(\xi=0.003\). Results indicate that inter-satellite THz-CVQSS can still maintain the reasonable performance in the finite-size scenario although the excess noise is comparatively high. We also plot the finite-size SKR of inter-satellite THz-CVQSS versus the reconciliation efficiency with different numbers of players in view of Figure 7. In the finite-size scenario, we set the block size \(M=10^{10}\) to demonstrate the available range of reconciliation efficiency. We find that as the number of players increases, the required reconciliation efficiency increases. For \(n=5\) and \(d=2000\) km, a \(10^{-4}\) bits/pulse finite-size SKR can be achieved with the reconciliation efficiency of at least \(0.93\). However, when \(n=10\), the required  
Figure 5: **(a)** The SKR of inter-satellite THz-CVQSS versus transmission distance (km) with different reconciliation efficiency and numbers of players. \(\xi_{0}=0.001,\eta=0.6,v_{el}=0.1,V_{M}=7\), and \(f=50\) THz. **(b)** The SKR of inter-satellite THz-CVQSS versus transmission distance (km) with different excess noise and numbers of players. \(\beta=0.98,\eta=0.6,v_{el}=0.1,V_{M}=7\), and \(f=50\) THz.