This paper studies a multiple-input multiple-output (MIMO) free-space optical (FSO) communication system employing continuous-variable quantum key distribution (CV-QKD), with the goal to support secret key transmission between two legitimate users, Alice and Bob. All involved wireless channels are subjected to atmospheric turbulence leading to beam spreading, pointing error, and turbulence-induced fading, which along with the presence of hybrid quantum noise negatively impact secret key exchange. Furthermore, the legitimate MIMO FSO system faces the threat of compromise from an eavesdropper, Eve, employing a collective Gaussian attack to intercept the secret key exchange. Novel one- and two-way protocols for enhancing the security of the transmitted keys are proposed. To this end, the transmissivity of the FSO channels is mathematically formulated and bounds on the mutual information between the transmitted and received coherent states are obtained, which are then used for deriving novel expressions for the secret key rates (SKRs) for both one- and two-way protocols. The presented numerical results corroborate the proposed analytical secrecy framework, quantifying the SKR gains obtained by employing MIMO and the two-way protocol for FSO CV-QKD systems.

翻译：本文研究了一种采用连续变量量子密钥分发（CV-QKD）的多输入多输出（MIMO）自由空间光（FSO）通信系统，旨在支持合法用户Alice与Bob之间的密钥传输。所有涉及的无线信道均受大气湍流影响，导致光束展宽、指向误差和湍流引起的衰落，这些因素与混合量子噪声的存在共同对密钥交换产生负面影响。此外，合法的MIMO FSO系统面临窃听者Eve的威胁，其采用集体高斯攻击来截获密钥交换。本文提出了增强传输密钥安全性的新型单向与双向协议。为此，我们对FSO信道的透射率进行了数学建模，并获得了发送与接收相干态之间互信息量的边界，进而推导出适用于单向与双向协议的密钥率（SKR）新表达式。所呈现的数值结果验证了所提出的分析保密框架，量化了在FSO CV-QKD系统中采用MIMO技术与双向协议所带来的密钥率增益。