On the quantum Renyi relative entropies and related capacity formulas

Details On the quantum Renyi relative entropies and related capacity formulas On the quantum Renyi relative entropies and related capacity formulas

2009-12-07

arxiv.org/abs/0912.1286v4

IEEE Transactions on Information Theory, vol. 57, 2474--2487, (2011)

Physics

Quantum Physics

v4: Cutoff rates are treated for correlated hypotheses, some proofs are given in greater detail

Scientific paper

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.

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