Information theoretic resource-breaking channels

Abstract

We propose the notion of process resource-breaking channels that break the resource for a quantum information processing task. We examine the same using quantum dense coding and teleportation protocols. We prove that the sets DBT (dense coding breaking) and TBT (teleportation breaking) are convex and compact and identify classical-quantum channels as their extreme points. We prove group-covariance to be a sufficient condition for channels to be DBT or TBT when they can destroy the resource of maximally entangled states. We present necessary and sufficient conditions for unital channels to be DBT for a single sender-receiver pair, while for multiple senders, the condition is sufficient. The set of qubit TBT channels is proved equivalent to qubit entanglement-breaking channels provided pre-processing is allowed. We construct witness operators to identify non-TBT(non-DBT) maps.