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 LEA, when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of L
_no
-EA√n-r
_no
-EA(n), r
_no
-EA(n) = o(√n), entanglement assistance allows L
_EA
√n log n - r
_EA
(n), rEA(n) = o(√n log n), covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the log n gain from our achievability; work on the matching converse is ongoing.