  We consider properties of quantum channels with use of unified entropies.
Extremal unravelings of quantum channel with respect to these entropies are
examined. The concept of map entropy is extended in terms of the unified
entropies. The map $(q,s)$-entropy is naturally defined as the unified
$(q,s)$-entropy of rescaled dynamical matrix of given quantum channel.
Inequalities of Fannes type are obtained for introduced entropies in terms of
both the trace and Frobenius norms of difference between corresponding
dynamical matrices. Additivity properties of introduced map entropies are
discussed. The known inequality of Lindblad with the entropy exchange is
generalized to many of the unified entropies. For tensor product of a pair of
quantum channels, we derive two-sided estimating of the output entropy of a
maximally entangled input state.
