Covariance matrices and the separability problem

Abstract

We propose a unifying approach to the separability problem using covariance matrices of locally measurable observables. From a practical point of view, our approach leads to strong entanglement criteria that allow to detect the entanglement of many bound entangled states in higher dimensions and which are at the same time necessary and sufficient for two qubits. From a fundamental perspective, our approach leads to insights into the relations between several known entanglement criteria -- such as the computable cross norm and local uncertainty criteria -- as well as their limitations.

4 pages, no figures; v3: final version to appear in PRL

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• Further results on entanglement detection and quantification from the correlation matrix criterion
• Observable estimation of entanglement for arbitrary finite-dimensional mixed states
• A class of inequalities inducing new separability criteria for bipartite quantum systems
• Iterations of nonlinear entanglement witnesses
• Separability and Entanglement of Quantum States Based on Covariance Matrices
• On the relation between Schmidt coefficients and entanglement
• Positive maps, majorization, entropic inequalities, and detection of entanglement
• Beyond the standard entropic inequalities: stronger scalar separability criteria and their applications
• Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics
• Extended Studies of Separability Functions and Probabilities and the Relevance of Dyson Indices
• A Note on Quantum Entanglement and PPT