Solution of the Convex Optimization Problem for Subcarrier Wave Continuous-Variable Quantum Key Distribution Protocol with Discrete Modulation

This paper introduces an approach to solving the convex optimization problem for subcarrier wave continuous-variable quantum key distribution (QKD) protocol using discrete modulation. For the first time, we provide a solution to this problem. By employing semidefinite programming, we have estimated the lower bound of the secure key generation rate in the asymptotic limit, taking into account an optimal attack from potential eavesdroppers. We considered an optical scheme that involves the use of quadrature phase modulation of coherent states and coherent detection based on the interference between the carrier and side frequencies. Our findings demonstrate the feasibility of distributing secure key generation rates over distances exceeding 100 km, even in the presence of realistic excess noise.