Bound Entanglement from Randomized Measurements

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 multiqubit 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.

Automated summary

In this study, systematic methods are presented to analyze different forms of entanglement in multiparticle quantum systems through random measurements and moments of probability distributions. Criteria for various forms of entanglement in three-qubit systems and multiqubit systems are optimized using second moments of randomized measurements. Additionally, criteria for detecting bound entangled states in higher-dimensional two-particle systems and higher moments are provided.