Separable states and positive maps

DOI10.1016/j.jfa.2007.12.017zbMath1143.46033arXiv0710.3071OpenAlexW2571167477MaRDI QIDQ2426510

Erling Størmer

Publication date: 22 April 2008

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0710.3071

zbMATH Keywords

states\(C^{*}\)-algebraspositive maps

Mathematics Subject Classification ID

Tensor products of (C^*)-algebras (46L06) States of selfadjoint operator algebras (46L30)

Related Items (24)

Constructing separable states in infinite-dimensional systems by operator matrices ⋮ A characterization of positive linear maps and criteria of entanglement for quantum states ⋮ Spectral properties of tensor products of channels ⋮ Entanglement witnesses constructed by permutation pairs ⋮ Entanglement-breaking channels with general outcome operator algebras ⋮ On a family of linear maps from \(M_n(\mathbb{C})\) to \(M_{n^2}(\mathbb{C})\) ⋮ Horodeckis criterion of separability of mixed states in von Neumann and C*-algebras ⋮ Eventually entanglement breaking maps ⋮ Formulas for calculating the extremum ranks and inertias of a four-term quadratic matrix-valued function and their applications ⋮ Cones with a mapping cone symmetry in the finite-dimensional case ⋮ Multiplicative properties of quantum channels ⋮ Convex cones in mapping spaces between matrix algebras ⋮ Arveson's work on entanglement ⋮ Entanglement witness criteria of strong-\(k\)-separability for multipartite quantum states ⋮ Finding decompositions of a class of separable states ⋮ FACIAL STRUCTURES FOR VARIOUS NOTIONS OF POSITIVITY AND APPLICATIONS TO THE THEORY OF ENTANGLEMENT ⋮ Constructing entanglement witnesses for states in Infinite-dimensional bipartite quantum systems ⋮ Characterization of partial positive transposition states and measures of entanglement ⋮ Cones of positive maps and their duality relations ⋮ Separability for positive operators on tensor product of Hilbert spaces ⋮ There is no direct generalization of positive partial transpose criterion to the three-by-three case ⋮ Constructing entanglement witnesses for infinite-dimensional systems ⋮ Tensor powers of 2-positive maps ⋮ Nullspaces of entanglement breaking channels and applications

Cites Work

• Extension of positive maps into B(\({\mathcal H})\)
• Decomposition of positive projections on C*-algebras
• Completely positive linear maps on complex matrices
• Positive semidefinite biquadratic forms
• Entangled states with positive partial transposes arising from indecomposable positive linear maps
• Separability criterion and inseparable mixed states with positive partial transposition.
• Construction of entangled states with positive partial transposes based on indecomposable positive linear maps
• Decomposable Positive Maps on C ∗ -Algebras
• Non-Decomposable Quantum Dynamical Semigroups and Bound Entangled States
• Entanglement Breaking Channels
• A family of indecomposable positive linear maps based on entangled quantum states
• Separability of \(n\)-particle mixed states: necessary and sufficient conditions in terms of linear maps
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