Entanglement-Saving Channels

TL;DR

This paper introduces and characterizes Entanglement Saving (ES) quantum channels that preserve entanglement under repeated application, and explores the subset of Asymptotic Entanglement Saving (AES) maps that maintain non-zero entanglement indefinitely.

Contribution

It provides a comprehensive structure theorem for ES channels and a complete characterization of AES maps, advancing understanding of entanglement preservation in quantum channels.

Findings

ES channels preserve entanglement under arbitrary repeated applications.

AES maps sustain a non-zero level of entanglement asymptotically.

Structural theorems fully characterize AES maps and nearly fully characterize ES channels.

Abstract

The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a maximally entangled configuration, preserve its entanglement even when applied an arbitrary number of times. In other words, a quantum channel $\psi$ is said to be ES if its powers $\psi^n$ are not entanglement-breaking for all integers $n$. We also characterize the properties of the Asymptotic Entanglement Saving (AES) maps. These form a proper subset of the ES channels that is constituted by those maps which, not only preserve entanglement for all finite $n$, but which also sustain an explicitly not null level of entanglement in the asymptotic limit~$n\rightarrow \infty$. Structure theorems are provided for ES and for AES maps which yield an almost complete characterization of the former and a full characterization of the latter.