  Werner states have a host of interesting properties, which often serve to
illuminate the unusual properties of quantum information. Starting from these
states, one may define a family of quantum channels, known as the Holevo-Werner
channels, which themselves afford several unusual properties. In this paper we
use the teleportation covariance of these channels to upper bound their two-way
assisted quantum and secret-key capacities. This bound may be expressed in
terms of relative entropy distances, such as the relative entropy of
entanglement, and also in terms of the squashed entanglement. Most
interestingly, we show that the relative entropy bounds are strictly
sub-additive for a sub-class of the Holevo-Werner channels, so that their
regularisation provides a tighter performance. These information-theoretic
results are first found for point-to-point communication and then extended to
repeater chains and quantum networks, under different types of routing
strategies.
