Objective The transmittance of free-space quantum channels plays an important role in the security analysis of continuous-variable quantum key distribution (CV-QKD). The atmospheric turbulence in free space leads to random fluctuations in transmittance, thereby degrading the CV-QKD. The existing analytical models fail to accurately characterize the transmittance of free-space quantum channel, since the models lack of comprehensive considerations based on the physical mechanism of atmospheric turbulence effects. Therefore, the accurate fluctuation characteristics of channel transmittance are studied in this paper by dint of numerical simulations concerning various turbulence impacts from the view of the basic concept of atmospheric turbulence.

Methods In this paper, the method of split-step transmission combined with phase screen flat panel is employed to numerically simulate the free space quantum channel according to the basic concept of atmospheric turbulence (Fig.2-3). The simulation results are comprehensively compared and analyzed with those existing analytical models. Concretely, numerical simulations of 10⁵ were performed on the free space quantum channel to calculate the transmission rate, and the mathematical statistics has been made. The probability density of the free space quantum channel transmission has been obtained (Fig.4-5).

Results and Discussions The results showed that the modified Von Karman atmospheric turbulence spectrum model could accurately achieve the realistic free space quantum channel, while the transmission of the free space quantum channel calculated using the Kolmogorov atmospheric turbulence spectrum model would be overestimated, with a maximum error of 5.28%. By comparing the probability density of transmission accurately achieved by numerical simulation with the existing elliptical beam approximation model and beam wandering model, it is concluded that those existed models would underestimate the transmission, thus deviating from the realistic free space quantum channels.

Conclusions The statistical characteristics of transmittance fluctuation with respect to the horizontal free space quantum channels under weak and moderate turbulence have been numerically studied in this paper by using the method of split-step transmission combined with the field amplitude sampling based on sparse spectrum. To begin with, the differences between the two widely known atmospheric turbulence spectrum models in simulating transmittance fluctuation have been analyzed. Compared to the modified spectrum model, the transmittances calculated by the Kolmogorov spectrum model are relatively higher. Consequently, the Kolmogorov spectrum model would overestimate the free space quantum channel transmittance, while the modified Von Karman spectrum model enables statistical laws of transmittance which highly match the realistic free space quantum channels. Subsequently, a comprehensive comparison has been performed between the statistical results associated with the numerical simulations and those known analytical models including the beam wandering model and the elliptical beam approximation model. It could be concluded that the probability density curves of transmittance presented by the existing analytical models deviate from the numerical simulation results. The transmittance would be underestimated by the use of existing models due to the fact that those models merely concern single turbulence effect. In contrast, the numerical simulations performed in the paper naturally take various turbulence impacts into account according to the basic concept of atmospheric turbulence. In the sense, the achievement is able to accurately represent the random fluctuation characteristics of free space quantum channel transmittance, which can be employed to precisely evaluate the security of free-space CV-QKD.