Asymptotic continuity of additive entanglement measures

TL;DR

This paper characterizes the optimal asymptotic transformation rates between pure entangled states using additive, asymptotically continuous entanglement measures, establishing their role as upper bounds.

Contribution

It demonstrates that for pure states, the optimal transformation rate equals the infimum of additive, asymptotically continuous entanglement measures' upper bounds.

Findings

Optimal rates characterized by entanglement measures

Additive asymptotically continuous measures bound transformation rates

Pure state transformations analyzed asymptotically

Abstract

We study rates asymptotic of transformations between entangled states by local operations and classical communication and a sublinear amount of quantum communication. It is known that additive asymptotically continuous entanglement measures provide upper bounds on the rates that are achievable with asymptotically vanishing error. We show that for transformations between pure states, the optimal rate between any pair of states can be characterized as the infimum of such upper bounds provided by fully additive asymptotically continuous entanglement measures.