title: 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.
authors.affiliation: Research Laboratory of Electronics, MIT, Cambridge, Massachusetts, USA. wlg@mit.edu
authors.forename: Ligong
authors.initials: L
authors.lastname: Wang
authors.forename: Renato
authors.initials: R
authors.lastname: Renner