Entanglement measures as physical observables

TL;DR

The paper explores how certain generalized observables can serve as directly measurable entanglement indicators for pure states and provide bounds for mixed states, bridging theoretical measures and experimental observability.

Contribution

It introduces a framework where generalized observables enable direct measurement of entanglement monotones, extending practical measurement techniques to mixed states.

Findings

General observables cannot serve as proper entanglement measures.

Generalized observables can measure entanglement in pure states.

Bounds on entanglement for mixed states can be experimentally obtained.

Abstract

We discuss why regular observables can not be proper entanglement measures, and how observables in a generalized setting can be used to make an entanglement monotone a directly observable quantity for the case of pure states. For the case of mixed states, these generalized observables can be used to find valid lower bounds on entanglement monotones that can be measured in laboratory experiments in the same fashion as it can also be done for pure states.