Covert Capacity of Bosonic Channels

We investigate the quantum-secure covert-communication capabilities of lossy thermal-noise bosonic channels, the quantum-mechanical model for many practical channels. We determine the expressions for the covert capacity of these channels: $L_{\text{no-EA}}$, when Alice and Bob share only a classical secret, and $L_{\text{EA}}$, when they benefit from entanglement assistance. We find that entanglement assistance alters the fundamental scaling law for covert communication. Instead of $L_{\text{no-EA}}\sqrt{n}-r_{\text{no-EA}}(n)$, $r_{\text{no-EA}}(n)=o(\sqrt{n})$, entanglement assistance allows $L_{\text{EA}}\sqrt{n}\log n-r_{\text{EA}}(n)$, $r_{\text{EA}}(n)=o(\sqrt{n}\log n)$, covert bits to be transmitted reliably over $n$ channel uses.