Irreducibly SU(2)-covariant quantum channels of low rank

Abstract

We investigate information theoretic properties of low rank (less than or equal to 3) quantum channels with SU(2)-symmetry, where we have a complete description. We prove that PPT property coincides with entanglement-breaking property and that degradability seldomly holds in this class. In connection with these results, we will demonstrate how we can compute Holevo and coherent information of those channels. In particular, we exhibit a strong form of additivity violation of coherent information, which resembles the superactivation of coherent information of depolarizing channels.