  Due to Csiszar and Koerner, the private capacity of classical wiretap
channels has a single-letter characterization in terms of the private
information. For quantum wiretap channels, however, it is known that
regularization of the private information is necessary to reach the capacity.
Here, we study hybrid classical-quantum wiretap channels in order to resolve to
what extent quantum effects are needed to witness non-additivity phenomena in
quantum Shannon theory. For wiretap channels with quantum inputs but classical
outputs, we prove that the characterization of the capacity in terms of the
private information stays single-letter. Hence, entangled input states are of
no asymptotic advantage in this setting. For wiretap channels with classical
inputs, we show by means of explicit examples that the private information
already becomes non-additive when either one of the two receivers becomes
quantum (with the other receiver staying classical). This gives non-additivity
examples that are not caused by entanglement and illustrates that quantum
adversaries are strictly different from classical adversaries in the wiretap
model.
