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arXiv · 1007.5456

One-Shot Classical-Quantum Capacity and Hypothesis Testing

Ligong Wang·Renato Renner
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Abstract

The one-shot classical capacity of a quantum channel quantifies the amount of classical information that can be transmitted through a single use of the channel such that the error probability is below a certain threshold. In this work, we show that this capacity is well approximated by a relative-entropy-type measure defined via hypothesis testing. Combined with a quantum version of Stein's lemma, our results give a conceptually simple proof of the well-known Holevo-Schumacher-Westmoreland theorem for the capacity of memoryless channels. More generally, we obtain tight capacity formulas for arbitrary (not necessarily memoryless) channels.

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Ligong Wang, Renato Renner. 2010-07-30. One-Shot Classical-Quantum Capacity and Hypothesis Testing. https://doi.org/10.1103/physrevlett.108.200501

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