Rank properties of exposed positive maps

DOI10.1080/03081087.2012.721360zbMath1279.47076arXiv1103.3497OpenAlexW3099322347MaRDI QIDQ2850990

Marcin Marciniak

Publication date: 1 October 2013

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.3497

zbMATH Keywords

completely positivepositive mapsexposedextremal

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Operator spaces and completely bounded maps (46L07) Positive linear operators and order-bounded operators (47B65) Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces (47H07) Quantum coherence, entanglement, quantum correlations (81P40) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items (10)

Merging of positive maps: a construction of various classes of positive maps on matrix algebras ⋮ On Extremal Positive Maps of Three-Dimensional Matrix Algebra ⋮ On a New Family of Extremal Positive Maps of Three-Dimensional Matrix Algebra ⋮ Construction of exposed indecomposable positive linear maps between matrix algebras ⋮ On the structure of positive maps. II. Low dimensional matrix algebras ⋮ Indecomposable exposed positive bi-linear maps between two by two matrices ⋮ The structural physical approximation conjecture ⋮ Dimension formula for induced maximal faces of separable states and genuine entanglement ⋮ Compositions and tensor products of linear maps between matrix algebras ⋮ Exposedness of Choi-Type Entanglement Witnesses and Applications to Lengths of Separable States

Cites Work

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• Positive Projections on C^∗ -Algebras and an Extremal Positive Map
• Duality for positive linear maps in matrix algebras
• Exposed positive maps: a sufficient condition
• Extremals and exposed faces of the cone of positive maps

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