On the quantum Renyi relative entropies and related capacity formulas

Following Csiszár's approach in classical information theory, it is shown that the quantum α-relative entropies with parameter α ∈ (0,1) can be represented as generalized cutoff rates, and hence a direct operational interpretation of the quantum α-relative entropies are provided. It is also shown that various generalizations of the Holevo capacity, defined in terms of the α-relative entropies, coincide for the parameter range α ∈ (0,2], and an upper bound on the one-shot ε-capacity of a classical-quantum channel in terms of these capacities is given.