为了研究大气湍流对自由空间量子密钥分发的性能影响, 将大气湍流建模为空间中随机分布的空气球泡, 利用几何光学原理分析单光子在湍流球泡中的传播, 定量计算了经过两次折射后由于偏振态变化造成的光子透射率比值k和误码率Ep的起伏, 利用蒙特卡洛方法模拟了湍流折射率随机变化时二者的趋势; 最后推导了经过湍流折射后的诱骗态空间量子密钥分发成码率公式并通过分析误码来源得到满足成码率需要的k值上限, 建立偏振误码率与入射角和湍流折射率的关系并得到Ep的安全阈值.仿真结果表明当入射角在44.8°~76.5°, 湍流折射率在1~1.33范围内可以满足误码率的上限约束.该研究为湍流条件下进行空间量子通信实验提供了理论参考.

In order to analyze the influence of atmospheric turbulence on the performance of free space Quantum Key Distribution (QKD), the turbulence is modeled as randomly distributed atmospheric bubbles so as to conceive the propagation process of single photon using geometric optics. The fluctuation of photon transmission ratio k and Quantum Bit Error Rate (QBER) Ep has been quantitatively calculated, which both are caused by the change of polarization state after continuous refractions. Then the trends of these two values are simulated with random turbulence refractive index using Monte Carlo method. Furthermore, the key generation rate of decoy state free space QKD has been derived under turbulence situation. The upper bound of k is achieved through analyzing the source of QBER and the relationship between Ep and incident angle and turbulence refractive index is established which defines the secure threshold of Ep. Simulation results show that when incident angle is between 44.8° and 76.5° while the refractive index falls within 1~1.33 will meet the required upper bound of Ep, which provides theoretical reference to quantum communication in turbulence scenario.