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

TL;DR

This paper establishes upper bounds on the quantum and secret-key capacities of Holevo-Werner channels using teleportation covariance and relative entropy measures, revealing sub-additivity and extending results to networks.

Contribution

It introduces new upper bounds for Holevo-Werner channels' capacities based on relative entropy measures and demonstrates their sub-additivity, extending to network scenarios.

Findings

Relative entropy bounds are strictly sub-additive for certain channels.

Regularisation yields tighter capacity bounds.

Results extend from point-to-point to networks and repeater chains.

Abstract

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.