# On the quantum Renyi relative entropies and related capacity formulas - Quantum Physics

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Abstract: We show that the quantum $\alpha$-relative entropies with parameter$\alpha\in 0,1$ can be represented as generalized cutoff rates in the senseof I. Csiszar, IEEE Trans. Inf. Theory 41, 26-34, 1995, which provides adirect operational interpretation to the quantum $\alpha$-relative entropies.We also show that various generalizations of the Holevo capacity, defined interms 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 ofa classical-quantum channel in terms of these capacities.

Autor: M. Mosonyi, F. Hiai

Fuente: https://arxiv.org/