Correlations between outcomes of random measurements

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.