Unified approach to geometric and positive-map-based non-linear entanglement identifiers
arXiv:1802.00806 · doi:10.1103/PhysRevA.97.042339
Abstract
Detecting quantumness of correlations (especially entanglement) is a very hard task even in the simplest case i.e. two-partite quantum systems. Here we provide an analysis whether there exists a relation between two most popular types of entanglement identifiers: the first one based on positive maps and not directly applicable in laboratory and the second one --- geometric entanglement identifier which is based on specific Hermiticity-preserving maps. We show a profound relation between those two types of entanglement criteria. Hereunder we have proposed a general framework of nonlinear functional entanglement identifiers which allows us to construct new experimentally friendly entanglement criteria.
arXiv comment11 pages, 3 figures
References in corpus (22)
- Quantum entanglement
- Separability Criterion for Density Matrices
- Separability of Mixed States: Necessary and Sufficient Conditions
- Entanglement detection
- Information-theoretic aspects of quantum inseparability of mixed states
- Taming multiparticle entanglement
- Separability of n-particle mixed states: necessary and sufficient conditions in terms of linear maps
- Experimental detection of entanglement via witness operators and local measurements
- Witnessing genuine multipartite entanglement with positive maps
- Experimentally friendly geometrical criteria for entanglement
- Class of PPT bound entangled states associated to almost any set of pure entangled states
- Genuine-multipartite entanglement criteria based on positive maps
- Note on Separability of the Werner states in arbitrary dimensions
- Correlation tensor criteria for genuine multiqubit entanglement
- Detecting genuine multipartite entanglement of pure states with bipartite correlations
- Experimental Schmidt Decomposition and Entanglement Detection
- Accessible nonlinear entanglement witnesses
- Nonlinear entanglement witnesses, covariance matrices and the geometry of separable states
- Iterations of nonlinear entanglement witnesses
- A unified approach to entanglement criteria using the Cauchy-Schwarz and Hölder inequalities
- Entanglement witnesses with variable number of local measurements
- Correlation-based entanglement criterion in bipartite multiboson systems