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. We determine the single-letter expressions for $L_{\rm SRL}$ and $J_{\rm SRL}$, and establish conditions when $J_{\rm SRL}=0$ (i.e., no pre-shared secret is needed). Finally, we evaluate the scenarios where covert communication is not governed by the SRL.

翻译：我们研究了在固定有限大小输入字母表的一般无记忆经典-量子信道上的隐蔽通信。当使用$n$个输入态的张量积时，我们证明了平方根定律（SRL）在此设定下主导隐蔽通信：在$n$次经典-量子信道使用中，最多可可靠传输$L_{\rm SRL}\sqrt{n}+o(\sqrt{n})$个隐蔽比特（且不能更多），其中$L_{\rm SRL}>0$是一个依赖于信道的常数，我们称之为隐蔽容量。我们还证明，为确保隐蔽性，通信双方在传输前需要共享$J_{\rm SRL}\sqrt{n}+o(\sqrt{n})$比特的秘密信息，其中$J_{\rm SRL}\geq0$是一个依赖于信道的常数。我们假设敌手具有量子计算能力，可对所有$n$次信道使用执行任意的联合（纠缠）测量。我们确定了$L_{\rm SRL}$和$J_{\rm SRL}$的单字母表达式，并建立了$J_{\rm SRL}=0$（即无需预共享秘密）的条件。最后，我们评估了隐蔽通信不受SRL主导的场景。