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An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization
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SYSNO ASEP 0440874 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název An interpolation problem for completely positive maps on matrix algebras: solvability and parametrization Tvůrce(i) Ambrozie, Calin-Grigore (MU-W) RID, SAI
Gheondea, A. (RO)Zdroj.dok. Linear & Multilinear Algebra - ISSN 0308-1087
Roč. 63, č. 4 (2015), s. 826-851Poč.str. 26 s. Jazyk dok. eng - angličtina Země vyd. GB - Velká Británie Klíč. slova Choi matrix ; completely positive ; density matrix Vědní obor RIV BA - Obecná matematika CEP IAA100190903 GA AV ČR - Akademie věd Institucionální podpora MU-W - RVO:67985840 UT WOS 000346350900012 EID SCOPUS 84919842384 DOI 10.1080/03081087.2014.903253 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2015
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