Fundamental Limits of Covert Communication Over Classical-Quantum Channels

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 a of n input states is used: L_SRL (Formula Presented) covert bits (but no more) can be reliably transmitted in n uses of classical-quantum channel, where L_SRL > 0 is a channel-dependent constant that we call covert capacity. We also show that ensuring covertness requires J_SRL (Formula Presented) bits secret key shared by the communicating parties prior to transmission, where J_SRL ≥ 0 is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on all n channel uses. We determine the single-letter expressions for L_SRL and J_SRL, and establish conditions when J_SRL = 0 (i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.