Bound entanglement from randomized measurements

TL;DR

This paper develops optimized methods to detect various forms of entanglement, including bound entanglement, in multiparticle quantum systems using moments from randomized measurements, even with limited control.

Contribution

It introduces systematic, optimized criteria for identifying different types of entanglement, including bound entanglement, based on moments of randomized measurement outcomes.

Findings

Optimal criteria for multiparticle entanglement detection in three-qubit systems.

Inequalities for bipartite entanglement analysis in multi-qubit systems.

Detection of bound entangled states in higher-dimensional systems.

Abstract

If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present systematic methods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements. Second, we present the optimal inequalities if entanglement in a bipartition of a multi-qubit system shall be analyzed in terms of these moments. Finally, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework.