We show that the quantum α-relative entropies with parameter
α∈(0,1) can be represented as generalized cutoff rates in the sense
of [I. Csiszar, IEEE Trans. Inf. Theory 41, 26-34, (1995)], which provides a
direct operational interpretation to the quantum α-relative entropies.
We also show that various generalizations of the Holevo capacity, defined in
terms of the α-relative entropies, coincide for the parameter range
α∈(0,2], and show an upper bound on the one-shot epsilon-capacity of
a classical-quantum channel in terms of these capacities.Comment: v4: Cutoff rates are treated for correlated hypotheses, some proofs
are given in greater detai