Correlations between outcomes of random measurements

TL;DR

This paper advances the understanding of multipartite quantum correlations from random measurements, deriving their maximal bounds, analyzing their behavior under local operations, and applying them to entanglement detection in mixed states.

Contribution

It develops a comprehensive framework for correlations from random measurements, including bounds, properties, and practical entanglement detection methods for mixed quantum states.

Findings

Correlations can detect entanglement in pure and some mixed states.

Maximal correlations are derived and shown to be non-monotonic under LOCC.

A closed-form condition for entanglement in rank-2 states is provided.

Abstract

We recently showed that multipartite correlations between outcomes of random observables detect quantum entanglement in all pure and some mixed states. In this followup article we further develop this approach, derive a maximal amount of such correlations, and show that they are not monotonous under local operations and classical communication. Nevertheless, we demonstrate their usefulness in entanglement detection with a single random observable per party. Finally we study convex-roof extension of the correlations and provide a closed-form necessary and sufficient condition for entanglement in rank-2 mixed states and a witness in general.