SKR Analysis of MIMO FSO Systems with One- and Two-way CV-QKD Protocols in Hybrid Quantum Noise Environment

A multiple-input multiple-output (MIMO) free-space optical (FSO) communication system is considered in this paper, which supports the secret key transmission between two legitimate users, Alice and Bob, by employing continuous-variable quantum key distribution (CV-QKD). The wireless channels are subjected to the effects of atmospheric turbulence that lead to beam spreading, pointing error, and turbulence-induced fading, which, along with the presence of hybrid quantum noise, negatively impact the secret key exchange between Alice and Bob. Furthermore, the security of the communication system is considered to be compromised due to the intervention of an eavesdropper, Eve, employing a collective Gaussian attack to intercept the secret key exchange. For this system, novel one-way and two-way protocols are proposed to enhance the security of the transmitted keys. The transmissivity of the FSO channels is mathematically formulated, and the bounds on the mutual information between the transmitted and received coherent states are obtained, using which, novel expressions for the secret key rates (SKRs) for the one-way and two-way protocols are derived. Asymptotic expressions for the SKRs and numerical results corroborating the analytical framework are also presented, which demonstrate the SKR gains obtained by employing MIMO and the two-way protocol for the FSO CV-QKD system.