On a family of linear maps from \(M_n(\mathbb{C})\) to \(M_{n^2}(\mathbb{C})\)

DOI10.1016/j.laa.2018.06.011zbMath1406.15005arXiv1802.07553OpenAlexW2788226205MaRDI QIDQ1654419

Hiroyuki Osaka, Gunjan Sapra, Benoit Collins

Publication date: 8 August 2018

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

Full work available at URL: https://arxiv.org/abs/1802.07553

zbMATH Keywords

decomposabilityequivariance property\(k\)-positivity

Mathematics Subject Classification ID

Positive matrices and their generalizations; cones of matrices (15B48) Positive linear operators and order-bounded operators (47B65) Linear transformations, semilinear transformations (15A04) Quantum coherence, entanglement, quantum correlations (81P40) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items (8)

Temperley-Lieb quantum channels ⋮ Schoenberg correspondence for \(k\)-(super)positive maps on matrix algebras ⋮ A class of optimal positive maps in \(M_n\) ⋮ Asymptotic analysis for \(O_N^+\)-Temperley-Lieb quantum channels ⋮ Mapping cone of \(k\)-entanglement breaking maps ⋮ Characterization of equivariant maps and application to entanglement detection ⋮ Best approximation of \(\kappa \)-random operator inequalities in matrix MB-algebras ⋮ Positive maps from irreducibly covariant operators

Cites Work

• Unnamed Item
• All 2-positive linear maps from \(M_3(\mathbb{C})\) to \(M_3(\mathbb{C})\) are decomposable
• Linear maps respecting unitary conjugation
• Completely positive linear maps on complex matrices
• Positive maps of low dimensional matrix algebras
• Separability of mixed states: necessary and sufficient conditions.
• Separable states and positive maps
• Linear transformations which preserve trace and positive semidefiniteness of operators
• Positive Linear Maps of Operator Algebras
• FACIAL STRUCTURES FOR VARIOUS NOTIONS OF POSITIVITY AND APPLICATIONS TO THE THEORY OF ENTANGLEMENT
• Positive Linear Maps on C^*-Algebras

This page was built for publication: On a family of linear maps from \(M_n(\mathbb{C})\) to \(M_{n^2}(\mathbb{C})\)