Rescaling multipartite entanglement measures for mixed states

TL;DR

This paper investigates how multipartite entanglement measures for mixed states change under local operations, providing a method to compute these measures exactly for a broader class of states, especially those with degree 2 homogeneity.

Contribution

It extends the understanding of entanglement measures' behavior under local operations and offers a way to calculate these measures exactly for more mixed states.

Findings

Enlarges the set of mixed states with exactly calculable entanglement measures.

Highlights the significance of measures with homogeneous degree 2 in state coefficients.

Provides a framework for analyzing the impact of local operations on entanglement measures.

Abstract

A relevant problem regarding entanglement measures is the following: Given an arbitrary mixed state, how does a measure for multipartite entanglement change if general local operations are applied to the state? This question is nontrivial as the normalization of the states has to be taken into account. Here we answer it for pure-state entanglement measures which are invariant under determinant 1 local operations and homogeneous in the state coefficients, and their convex-roof extension which quantifies mixed-state entanglement. Our analysis allows to enlarge the set of mixed states for which these important measures can be calculated exactly. In particular, our results hint at a distinguished role of entanglement measures which have homogeneous degree 2 in the state coefficients.