Capacity Theorems for Covert Bosonic Channels

We study quantum-secure covert-communication over lossy thermal-noise bosonic channels, the quantum-mechanical model for many practical channels. We derive the expressions for the covert capacity of these channels: L no-EA , when Alice and Bob share only a classical secret, and L EA , when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of ${L_{{\text{no - EA}}}}\sqrt n - {r_{{\text{no - EA}}}}\left( n \right)$, ${r_{{\text{no - EA}}}}\left( n \right) = o\left( {\sqrt n } \right)$, entanglement assistance allows ${L_{{\text{EA}}}}\sqrt n \log n - {r_{{\text{EA}}}}\left( n \right)$, ${r_{{\text{EA}}}}\left( n \right) = o\left( {\sqrt n \log n} \right)$, covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the logn gain from our achievability; work on the matching converse is ongoing.