  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.
