Continuous-variable quantum key distribution (CV-QKD) protocols have demonstrated the potential to achieve higher secure key rates in fiber-optic channels. However, the feasibility of satellite-to-ground Gaussian-modulated CV-QKD (GM CV-QKD) remains largely theoretical research and has only undergone preliminary experimental investigation. Practical factors, such as atmospheric attenuation, diffraction, and turbulence, play a significant role in the feasibility of satellite-to-ground CV-QKD protocols. Furthermore, the limited access time between low-Earth orbit satellites and ground stations exacerbates the effects of finite key length on the estimation of protocol parameters.

This study assesses the feasibility of satellite-to-ground GM CV-QKD by developing a dynamic, time-varying orbital model for satellite downlinks, based on realistic performance parameters of satellites and ground stations. This study examines the effects of preparation variance and reverse reconciliation efficiency on key generation and compares the performance of GM CV-QKD with discrete variable QKD (DV-QKD). Considering the rapid motion of the satellite, which limits the access time of the system, this study also examines the influence of the symbol number of parameter estimation and symbol transmission rate on the key generation under the finite key length effect to optimize the system performance.

Based on the theoretical model and specific simulation parameters, the following simulations are conducted: Fig. 4 examines the effects of preparation variance and reverse negotiation efficiency on key generation. For any communication system with different negotiation efficiencies, there is an optimal preparation variance that maximizes the total key generation of the system. Fig. 5 compares optical fiber CV-QKD and free space CV-QKD, revealing that free space CV-QKD decreases the mutual information of the communication parties and reduces the protocol performance due to fluctuating channels. Fig. 6 compares satellite-to-ground DV-QKD and GM CV-QKD, demonstrating that GM CV-QKD significantly outperforms DV-QKD in Earth-to-Earth communication with low-Earth orbit satellites and high noise levels. Fig. 7 explores the influence of the number of symbols used for parameter estimation and the symbol transmission rate on key generation under the finite key length effect and optimizes the number of symbol symbols for parameter estimation under different symbol transmission rates.

This study investigates the influence of preparation variance and reverse negotiation efficiency on key generation using a satellite-Earth orbit model. The findings reveal that compared with fiber CV-QKD, the random fluctuation in the free space channel reduces the mutual information of the two communication parties. In addition, due to the spatial channel is fluctuating, the effect of preparation variance on the key generation rate is not single, and there is an optimal preparation variance. A comparison between GM CV-QKD and DV-QKD shows that GM CV-QKD significantly outperforms DV-QKD in low-Earth orbit satellite communication scenarios with a little excess noise. The effect of finite key length is examined, and the effect of symbol transmission rate and the number of estimated symbols on the system performance is analyzed. The simulation results indicate that the symbol transmission rate must exceed a threshold to generate the positive key. In addition, when the symbol transmission rate is in the nonlinear growth region, increasing the symbol transmission rate can bring more benefits. The optimal number of symbols for parameter estimation at different symbol transmission rates is determined to improve system performance. These findings offer valuable insights for the design and optimization of the satellite-to-ground GM-CV-QKD experiment.