Information Theoretic Representations of Qubit Channels

Abstract

A set of qubit channels has a classical representation when it is isomorphic to the convex closure of a group of classical channels. From Crowder and Martin (Proceedings of Quantum Physics and Logic, Electronic Notes in Theoretical Computer Science, 2009), we know that up to isomorphism there are five such sets, each corresponding to either a subgroup of the alternating group on four letters, or a subgroup of the symmetric group on three letters. In this paper, we show that the classical representation of a qubit channel also carries its information theoretic data—in particular, both the Holevo capacity and the scope of a unital qubit channel can be completely calculated from a systematically determined classical channel.