Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.

中文翻译：

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考虑大气湍流和指向误差的 FSO 信道上的混合 MPPM-BB84 量子密钥分发


如今，关键信息的传输需要高水平的安全性。量子密钥分发（QKD）系统被认为是保护此类信息的最佳选择。许多研究表明受多进制脉冲位置调制 (MPPM) 启发的 QKD 光纤的效率。自由空间光 (FSO) 链路提供高效且有效的数据传输系统。然而，激光束发散、未对准和湍流引起的衰落对 FSO 链路中接收辐照度的累积影响可能会使位于授权接收器附近的外部窃听者在某些条件下破坏传输。本文介绍了基于 MPPM 和 BB84 协议 (MPPM-BB84) 的 FSO 系统在具有指向误差的 Gamma-Gamma (GG) 湍流通道上的开发。使用 MPPM 实现时间分级，以提高系统安全性并降低量子误码率 (QBER)。研究了光子数分裂攻击和过量噪声下的系统安全性。引入了平均符号错误概率（SER）、原始密钥率（RKR）和秘密密钥率（SKR）的渐近表达式的封闭式表达式。此外，蒙特卡洛模拟还用于证明分析结果的有效性。每个符号长度的平均每脉冲光子数（达到最大RKR和SKR）的最佳值可以保证FSO系统在不同天气条件下的稳定性。较小的符号长度更能容忍检测器丢失。所提出的系统支持 1 公里到 3 公里的链接距离，同时保持 SKR 几乎恒定。