On the Quantum Renyi Relative Entropies and Related Capacity Formulas

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