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An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization
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SYSNO ASEP 0440874 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization Author(s) Ambrozie, Calin-Grigore (MU-W) RID, SAI
Gheondea, A. (RO)Source Title Linear & Multilinear Algebra - ISSN 0308-1087
Roč. 63, č. 4 (2015), s. 826-851Number of pages 26 s. Language eng - English Country GB - United Kingdom Keywords Choi matrix ; completely positive ; density matrix Subject RIV BA - General Mathematics R&D Projects IAA100190903 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) Institutional support MU-W - RVO:67985840 UT WOS 000346350900012 EID SCOPUS 84919842384 DOI 10.1080/03081087.2014.903253 Annotation We present certain existence criteria and parameterizations for an interpolation problem for completely positive maps that take given matrices from a finite set into prescribed matrices. Our approach uses density matrices associated to linear functionals on -subspaces of matrices, inspired by the Smith-Ward linear functional and Arveson's Hahn-Banach Type Theorem. A necessary and sufficient condition for the existence of solutions and a parametrization of the set of all solutions of the interpolation problem in terms of a closed and convex set of an affine space are obtained. Other linear affine restrictions, like trace preserving, can be included as well, hence covering applications to quantum channels that yield certain quantum states at prescribed quantum states. We also perform a careful investigation on the intricate relation between the positivity of the density matrix and the positivity of the corresponding linear functional. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2015
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