Secret Key Rate Analysis of RIS-Assisted THz MIMO CV-QKD Systems under Localized and Global Eavesdropping

A multiple-input multiple-output (MIMO) system operating at terahertz (THz) frequencies and consisting of a transmitter, Alice, that encodes secret keys using Gaussian-modulated coherent states, which are communicated to a legitimate receiver, Bob, under the assistance of a reconfigurable intelligent surface (RIS) is considered in this paper. The composite wireless channel comprising the direct Alice-to-Bob signal propagation path and the RIS-enabled reflected one is modeled as a passive linear Gaussian quantum channel, allowing for a unitary dilation that preserves the canonical commutation relations. The security of the considered RIS-empowered MIMO system is analyzed under collective Gaussian entangling attacks, according to which an eavesdropper, Eve, is assumed to have access to environmental modes associated with specific propagation segments. We also study, as a benchmark, the case where Eve has access to the purification of the overall channel. The legitimate receiver, Bob, is designed to deploy homodyne detection and reverse reconciliation for key extraction. Novel expressions for the achievable secret key rate (SKR) of the system are derived for both the considered eavesdropping scenarios. Furthermore, an optimization framework is developed to determine the optimal RIS phase configuration matrix that maximizes the SKR performance. The resulting optimization problem is efficiently solved using particle swarm optimization. Numerical results are presented to demonstrate the system's performance with respect to various free parameters. It is showcased that the considered RIS plays a crucial role in enhancing the SKR of the system as well as in extending the secure communication range. This establishes RIS-assisted THz MIMO CV-QKD as a promising solution for next generation secure wireless networks.