Strong converse exponent for classical-quantum channel coding

Abstract

We determine the exact strong converse exponent of classical-quantum channel coding, for every rate above the Holevo capacity. Our form of the exponent is an exact analogue of Arimoto's, given as a transform of the Renyi capacities with parameters alpha>1. It is important to note that, unlike in the classical case, there are many inequivalent ways to define the Renyi divergence of states, and hence the R\'enyi capacities of channels. Our exponent is in terms of the Renyi capacities corresponding to a version of the Renyi divergences that has been introduced recently in [M\"uller-Lennert, Dupuis, Szehr, Fehr and Tomamichel, J. Math. Phys. 54, 122203, (2013)], and [Wilde, Winter, Yang, Commun. Math. Phys. 331, (2014)]. Our result adds to the growing body of evidence that this new version is the natural definition for the purposes of strong converse problems.