The square root law (SRL) is the fundamental limit of covert communication
over classical memoryless channels (with a classical adversary) and quantum
lossy-noisy bosonic channels (with a quantum-powerful adversary). The SRL
states that O(n​) covert bits, but no more, can be reliably
transmitted in n channel uses with O(n​) bits of secret
pre-shared between the communicating parties. Here we investigate covert
communication over general memoryless classical-quantum (cq) channels with
fixed finite-size input alphabets, and show that the SRL governs covert
communications in typical scenarios. %This demonstrates that the SRL is
achievable over any quantum communications channel using a product-state
transmission strategy, where the transmitted symbols in every channel use are
drawn from a fixed finite-size alphabet. We characterize the optimal constants
in front of n​ for the reliably communicated covert bits, as well as
for the number of the pre-shared secret bits consumed. We assume a
quantum-powerful adversary that can perform an arbitrary joint (entangling)
measurement on all n channel uses. However, we analyze the legitimate
receiver that is able to employ a joint measurement as well as one that is
restricted to performing a sequence of measurements on each of n channel uses
(product measurement). We also evaluate the scenarios where covert
communication is not governed by the SRL