RIS-Assisted MIMO CV-QKD at THz Frequencies: Channel Estimation and Secret Key Rate Analysis

In this paper, a multiple-input multiple-output (MIMO) wireless system incorporating a reconfigurable intelligent surface (RIS) to efficiently operate at terahertz (THz) frequencies is considered. The transmitter, Alice, employs continuous-variable quantum key distribution (CV-QKD) to communicate secret keys to the receiver, Bob, who utilizes either homodyne or heterodyne detection. The latter node applies the least-squares approach to estimate the effective MIMO channel gain matrix prior to receiving the secret key, and this estimation is made available to Alice via an error-free feedback channel. An eavesdropper, Eve, is assumed to employ either a collective Gaussian entanglement attack or an individual attack on the feedback channel to obtain the estimated channel state information. We present novel closed-form expressions for the secret key rate (SKR) performance of the proposed RIS-assisted THz CV-QKD system. An optimization framework to obtain the optimal phase shifts of the RIS to maximize the SKR is proposed, and a particle-swarm optimization (PSO)-based algorithm is deployed to solve the optimization problem. The effect of various system parameters, such as the number of RIS elements and their phase configurations, the channel estimation error, and the detector noise, on the SKR performance is studied via numerical evaluation of the derived formula. It is demonstrated that the RIS contributes to larger SKR for larger link distances, and that heterodyne detection is preferable over homodyne at lower pilot symbol powers.