Dynamical Entanglement

TL;DR

This paper introduces measures for dynamical entanglement of bipartite channels, using the partial transpose of superchannels, and establishes their operational significance in channel simulation.

Contribution

It defines computable measures of dynamical entanglement and links them to the exact asymptotic dynamical entanglement cost, advancing understanding of quantum channel entanglement.

Findings

Negativity as a measure of dynamical entanglement

Max-logarithmic negativity equals the asymptotic entanglement cost

New measures characterize channel simulation conditions

Abstract

Unlike the entanglement of quantum states, very little is known about the entanglement of bipartite channels, called dynamical entanglement. Here we work with the partial transpose of a superchannel, and use it to define computable measures of dynamical entanglement, such as the negativity. We show that a version of it, the max-logarithmic negativity, represents the exact asymptotic dynamical entanglement cost. We discover a family of dynamical entanglement measures that provide necessary and sufficient conditions for bipartite channel simulation under local operations and classical communication and under operations with positive partial transpose.