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arXiv · 0912.1286

On the quantum Renyi relative entropies and related capacity formulas

M. Mosonyi·F. Hiai
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Abstract

We show that the quantum $α$-relative entropies with parameter $α\in (0,1)$ 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 $α$-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 $α\in (0,2]$, and show an upper bound on the one-shot epsilon-capacity of a classical-quantum channel in terms of these capacities.

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M. Mosonyi, F. Hiai. 2010-07-26. On the quantum Renyi relative entropies and related capacity formulas. https://doi.org/10.1109/tit.2011.2110050

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