  We study the identification capacity of classical-quantum channels
("cq-channels"), under channel uncertainty and privacy constraints. To be
precise, we consider first compound memoryless cq-channels and determine their
identification capacity; then we add an eavesdropper, considering compound
memoryless wiretap cqq-channels, and determine their secret identification
capacity. In the first case (without privacy), we find the identification
capacity always equal to the transmission capacity. In the second case, we find
a dichotomy: either the secrecy capacity (also known as private capacity) of
the channel is zero, and then also the secrecy identification capacity is zero,
or the secrecy capacity is positive and then the secrecy identification
capacity equals the transmission capacity of the main channel without the
wiretapper. We perform the same analysis for the case of arbitrarily varying
wiretap cqq-channels (cqq-AVWC), with analogous findings, and make several
observations regarding the continuity and super-additivity of the
identification capacity in the latter case.
