Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states
arXiv:quant-ph/0612108 · doi:10.1088/1742-6596/67/1/012004
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.
arXiv comment12 pages, 2 figures, for the proceedings of DICE2006 in Piombino (Italy)
References in corpus (14)
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Experimental One-Way Quantum Computing
- Scalable multi-particle entanglement of trapped ions
- Bell Inequalities and the Separability Criterion
- Optimization of entanglement witnesses
- Classification of mixed three-qubit states
- Witnessing multipartite entanglement
- Violation of local uncertainty relations as a signature of entanglement
- Inseparability criteria for bipartite quantum states
- Detection of entanglement with few local measurements
- Nonlinear entanglement witnesses
- Entanglement verification for quantum key distribution systems with an underlying bipartite qubit-mode structure
- Quantum Separability and Entanglement Detection via Entanglement-Witness Search and Global Optimization
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