Information theoretic resource-breaking channels

TL;DR

This paper introduces the concept of resource-breaking channels in quantum information, characterizes their properties, and provides conditions for channels to break resources like entanglement in dense coding and teleportation.

Contribution

It defines and analyzes resource-breaking channels, proves their convexity and compactness, and identifies conditions under which channels break quantum resources.

Findings

Sets of dense coding and teleportation breaking channels are convex and compact.

Classical-quantum channels are extreme points of these sets.

Group-covariance is sufficient for resource-breaking in certain 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.