Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states

Abstract

Entanglement witnesses provide a standard tool for the analysis of entanglement in experiments. We investigate possible nonlinear entanglement witnesses from several perspectives. First, we demonstrate that they can be used to show that the set of separable states has no facets. Second, we give a new derivation of nonlinear witnesses based on covariance matrices. Finally, we investigate extensions to the multipartite case.

12 pages, 2 figures, for the proceedings of DICE2006 in Piombino (Italy)

References in corpus (2)

• Scalable multi-particle entanglement of trapped ions
• Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization

Cited by in corpus (8)

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• Iterations of nonlinear entanglement witnesses
• Efficient nonlinear witnessing of non-absolutely separable states with lossy detectors
• Nonlinear Improvement of Qubit-qudit Entanglement Witnesses
• Separable Ball around any Full-Rank Multipartite Product State
• Measurement-device-independent nonlinear entanglement witnesses
• Closing loopholes of measurement-device-independent nonlinear entanglement witnesses