Quantum Covert Communication with Quantum GUS States

Quantum covert communication aims to enable undetectable information transfer by concealing the very act of communication, making it a critical paradigm for applications where undetectability is essential. Implementing quantum covert communication in realistic scenarios, such as in free-space optical networks necessitate rigorous analysis of how quantum states evolve through noisy channels and how optimal measurement strategies can be designed to recover transmitted information reliably. In this work, we investigate the performance of quantum covert communication employing geometrically uniform symmetry (GUS) states encoded in a d-rail bosonic system over lossy thermal-noise channels. We analytically derive the transformation of the GUS states through the channel and show that the overall effect is equivalent to a depolarizing channel. To assess state distinguishability, we develop an optimal measurement strategy based on minimum quadratic error, and find the analytical expressions for the correct decision probability.