In this paper, we investigate the transmission probabilities in three cases (depending only on the legitimate receiver, depending only the eavesdropper, and depending on both legitimate receiver and eavesdropper) in quantum key distribution (QKD) systems over free-space optical links. To be more realistic, we consider a generalized pointing error scenario, where the azimuth and elevation pointing error angles caused by stochastic jitters and vibrations in the legitimate receiver platform are independently distributed according to a non-identical normal distribution. Taking these assumptions into account, we derive approximate expressions of transmission probabilities by using the Gaussian quadrature method. To simplify the expressions and get some physical insights, some asymptotic analysis on the transmission probabilities is presented based on asymptotic expression for the generalized Marcum Q-function when the telescope gain at the legitimate receiver approaches to infinity. Moreover, from the asymptotic expression for the generalized Marcum Q-function, the asymptotic outage probability over Beckmann fading channels (a general channel model including Rayleigh, Rice, and Hoyt fading channels) can be also easily derived when the average signal-to-noise ratio is sufficiently large, which shows the diversity order and array gain.

中文翻译：

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FSO链路上量子密钥分发系统的传输概率

在本文中，我们研究了在自由空间光链路上的量子密钥分发 (QKD) 系统中三种情况下的传输概率（仅取决于合法接收者、仅取决于窃听者、取决于合法接收者和窃听者）。为了更现实，我们考虑了一个广义指向误差场景，其中由合法接收器平台中的随机抖动和振动引起的方位角和仰角指向误差角根据不相同的正态分布独立分布。考虑到这些假设，我们通过使用高斯正交方法推导出传输概率的近似表达式。为了简化表达式并获得一些物理见解，当合法接收器处的望远镜增益接近无穷大时，基于广义 Marcum Q 函数的渐近表达式，对传输概率进行了一些渐近分析。此外，从广义 Marcum Q 函数的渐近表达式，也可以很容易地推导出 Beckmann 衰落信道（包括 Rayleigh、Rice 和 Hoyt 衰落信道的通用信道模型）上的渐近中断概率，当平均信噪比为ratio 足够大，说明分集阶数和阵列增益。