Towards a Characterization of the Covert Capacity of Bosonic Channels under Trace Distance

We characterize upper and lower bounds for the covert capacity of lossy thermal-noise bosonic channels when measuring covertness using fidelity and trace distance. Although we fall short of characterizing the exact covert capacity, we also provide bounds on the number of secret-key bits required to achieve covertness. The bounds are established by combining recent quantum information theory results in separable Hilbert spaces, including position based coding (Oskouei et al., arXiv: 1804.08144 [1]), convex splitting (Khatri et al., arXiv: 1910.03883 [2]), and perturbation theory (Grace and Guha, arXiv: 2106.05533 [3]).