On superactivation of zero-error capacities and reversibility of a quantum channel

TL;DR

This paper presents examples of quantum channels exhibiting superactivation of zero-error capacities, explores conditions preventing superactivation, and discusses implications for channel reversibility, using advanced mathematical tools for both finite and infinite dimensions.

Contribution

It introduces new low-dimensional quantum channels demonstrating superactivation and analyzes conditions under which capacities cannot be superactivated, extending understanding of quantum channel behaviors.

Findings

Demonstrated superactivation of zero-error capacities in specific quantum channels.

Identified classes of channels where superactivation is impossible.

Linked superactivation phenomena to channel reversibility and analyzed implications.

Abstract

We propose examples of low dimensional quantum channels demonstrating different forms of superactivation of one-shot zero-error capacities, in particular, the extreme superactivation (this complements the recent result of T.S.Cubitt and G.Smith). We also describe classes of quantum channels whose zero-error classical and quantum capacities cannot be superactivated. We consider implications of the superactivation of one-shot zero-error capacities to analysis of reversibility of a tensor-product channel with respect to families of pure states. Our approach based on the notions of complementary channel and of transitive subspace of operators makes it possible to study the superactivation effects for infinite-dimensional channels as well.