On the continuity of asymptotic measures of entanglement

TL;DR

This paper proves that all asymptotic entanglement measures are continuous within any open set of distillable states, despite their definition involving the limit of many copies of the state.

Contribution

It establishes the continuity of asymptotic entanglement measures in open sets of distillable states, clarifying their mathematical behavior.

Findings

Asymptotic entanglement measures are continuous in open sets of distillable states.

Continuity holds even though measures are defined via large N limits.

Provides theoretical insight into the stability of entanglement quantification.

Abstract

We show that, in any open set of distillable states, all asymptotic entanglement measures $E(\rho)$ are continuous as a function of (a single copy of) $\rho$, even though they quantify the entanglement properties of $\rho^{\otimes N}$ is the large $N$ limit.