Conditional Entanglement

TL;DR

This paper introduces a new class of entanglement measures called conditional entanglement, derived from quantum extension and conditioning, which are convex, super-additive, and can be constructed from correlation measures.

Contribution

It presents a generic framework for constructing conditional entanglement measures that are convex, super-additive, and extend to multipartite systems, advancing entanglement quantification methods.

Findings

New entanglement measures are convex and super-additive.

Measures can be built directly from correlation measures.

Framework generalizes to multipartite entanglement.

Abstract

Based on the ideas of {\it quantum extension} and {\it quantum conditioning}, we propose a generic approach to construct a new kind of entanglement measures called {\it conditional entanglement}. The new measures, built from the known entanglement measures, are convex, automatically {\it super-additive}, and even smaller than the regularized versions of the generating measures. More importantly, new measures can also be built directly from measures of correlations, enabling us to introduce an {\it additive} measure and generalize it to a multipartite entanglement measure.