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Werner states have a host of interesting properties, which often serve toilluminate the unusual properties of quantum information. Starting from thesestates, one may define a family of quantum channels, known as the Holevo-Wernerchannels, which themselves afford several unusual properties. In this paper weuse the teleportation covariance of these channels to upper bound their two-wayassisted quantum and secret-key capacities. This bound may be expressed interms of relative entropy distances, such as the relative entropy ofentanglement, and also in terms of the squashed entanglement. Mostinterestingly, we show that the relative entropy bounds are strictlysub-additive for a sub-class of the Holevo-Werner channels, so that theirregularisation provides a tighter performance. These information-theoreticresults are first found for point-to-point communication and then extended torepeater chains and quantum networks, under different types of routingstrategies.

Converse bounds for quantum and private communication over Holevo-Werner channels