Capacities of a two-parameter family of noisy Werner–Holevo channels

Abstract

In \(d=2j+1\) dimensions, the Landau–Streater quantum channel is defined on the basis of spin j representation of the su(2) algebra. Only for \(j=1\), this channel is equivalent to the Werner–Holevo channel and enjoys covariance properties with respect to the group SU(3). We extend this class of channels to higher dimensions in a way that is based on the Lie algebra so(d) and su(d). As a result, it retains its equivalence to the Werner–Holevo channel in arbitrary dimensions. The resulting channel is covariant with respect to the unitary group SU(d). We then modify this channel in a way that can act as a noisy channel on qudits. The resulting modified channel now interpolates between the identity channel and the Werner–Holevo channel, and its covariance is reduced to the subgroup of orthogonal matrices SO(d). We then investigate some of the properties of the resulting two-parameter family of channels, including their Holevo quantity, entanglement-assisted capacity, the zero-capacity region and a possible lower bound for their quantum capacity.