  We show that the quantum $\alpha$-relative entropies with parameter
$\alpha\in (0,1)$ 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 $\alpha$-relative entropies.
We also show that various generalizations of the Holevo capacity, defined in
terms of the $\alpha$-relative entropies, coincide for the parameter range
$\alpha\in (0,2]$, and show an upper bound on the one-shot epsilon-capacity of
a classical-quantum channel in terms of these capacities.
