Fundamental Limits of Covert Communication over Classical-Quantum Channels

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We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets.

• We show that the square root law (SRL) governs covert communication in this setting when product of $n$ input states is used: $L_{\rm SRL}\sqrt{n}+o(\sqrt{n})$ covert bits (but no more) can be reliably transmitted in $n$ uses of classical-quantum channel, where $L_{\rm SRL}>0$ is a channel-dependent constant that we call covert capacity.
• We also show that ensuring covertness requires $J_{\rm SRL}\sqrt{n}+o(\sqrt{n})$ bits secret shared by the communicating parties prior to transmission, where $J_{\rm SRL}\geq0$ is a channel-dependent constant.
• We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on all $n$ channel uses.