Strong Converse Exponent for Classical-Quantum Channel Coding

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 R,nyi capacities with parameters . It is important to note that, unlike in the classical case, there are many inequivalent ways to define the R,nyi divergence of states, and hence the R,nyi capacities of channels. Our exponent is in terms of the R,nyi capacities corresponding to a version of the R,nyi divergences that has been introduced recently in Muller-Lennert et al. (J Math Phys 54(12):122203, 2013.). Our result adds to the growing body of evidence that this new version is the natural definition for the purposes of strong converse problems.