One-Shot Classical-Quantum Capacity and Hypothesis Testing

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.

Additional references and slightly different version of Theorem 1

References in corpus (3)

• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• Noisy channel coding via privacy amplification and information reconciliation
• Generalized relative entropies and the capacity of classical-quantum channels

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