Conventionally, unconditional information security has been studied by quantum cryptography although the assumption of an omnipotent eavesdropper is too strict for some realistic implementations. In this paper, we study the realistic secret key distillation over a satellite-to-satellite free space optics channel where we assume a limited-sized aperture eavesdropper (Eve) in the same plane of the legitimate receiver (Bob) and determine the secret key rate lower bounds correspondingly. We first study the input power dependency without assumptions on Bob's detection scheme before optimizing the input power to determine lower bounds as functions of transmission distances, center frequency or Eve aperture radius. Then we calculate analytical expressions regarding the SKR lower bound and upper bound as transmission distance goes to infinity. We also incorporate specific discrete variable (DV) and continuous variable (CV) protocols for comparison. We demonstrate that significantly higher SKR lower bounds can be achieved compared to traditional unrestricted Eve scenario.

中文翻译：

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卫星到卫星自由空间光学信道上的秘密密钥蒸馏，在合法接收器的同一平面上有一个有限大小的孔径窃听器

传统上，量子密码学研究了无条件信息安全，尽管全能窃听者的假设对于某些现实实现来说过于严格。在本文中，我们研究了卫星到卫星自由空间光学信道上现实的秘密密钥蒸馏，我们假设在合法接收者 (Bob) 的同一平面上有一个有限大小的孔径窃听者 (Eve) 并确定秘密密钥率下限相应。在优化输入功率以确定作为传输距离、中心频率或 Eve 孔径半径的函数的下限之前，我们首先研究了输入功率依赖性，而不假设 Bob 的检测方案。然后我们计算关于 SKR 下界和上界的解析表达式，因为传输距离趋于无穷大。我们还结合了特定的离散变量 (DV) 和连续变量 (CV) 协议进行比较。我们证明，与传统的不受限制的 Eve 场景相比，可以实现更高的 SKR 下限。