Interpolation by completely positive maps

DOI10.1080/03081087.2011.585987zbMath1236.15004arXiv1012.1675OpenAlexW2031479886MaRDI QIDQ3104551

Chi-Kwong Li, Yiu-Tung Poon

Publication date: 14 December 2011

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

Full work available at URL: https://arxiv.org/abs/1012.1675

zbMATH Keywords

Hermitian matriceseigenvaluesmatrix inequalitiespositive semidefinitelinear preserver problemdilationscompletely positive mapmajorizationquantum informationunitary orbitsquantum operations

Mathematics Subject Classification ID

Inequalities involving eigenvalues and eigenvectors (15A42) Positive matrices and their generalizations; cones of matrices (15B48) Periodic orbits of vector fields and flows (37C27) Linear transformations, semilinear transformations (15A04) Linear preserver problems (15A86) Quantum information, communication, networks (quantum-theoretic aspects) (81P45)

Related Items

Strict positivity and D-majorization, The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra, Positive maps constructed from permutation pairs, Unnamed Item, Convex multivariate operator means, The range of generalized quantum operations, Complete order equivalence of spin unitaries, Projection methods for quantum channel construction, Dilation theory: a guided tour, Entropy, stochastic matrices, and quantum operations, Completely positive interpolations of compact, trace-class and Schatten-\(p\) class operators, Some characterizations of quantum channel in infinite Hilbert spaces, A new criterion and a special class of \(k\)-positive maps, An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization, Extension properties of some completely positive maps, Physical transformations between quantum states

Cites Work

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• Principal Submatrices of a Hermitian Matrix
• Numerical ranges and dilations^∗
• Eigenvalues, singular values, and Littlewood-Richardson coefficients
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix