Roots of completely positive maps

Bhat, B.V.R. and Hillier, Robin and Mallick, Nirupama and U., Vijaya Kumar (2020) Roots of completely positive maps. Linear Algebra and its Applications, 587. pp. 143-165. ISSN 0024-3795

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We introduce the concept of completely positive roots of completely positive maps on operator algebras. We do this in different forms: as asymptotic roots, proper discrete roots and as continuous one-parameter semigroups of roots. We present structural and general existence and non-existence results, some special examples in settings where we understand the situation better, and several challenging open problems. Our study is closely related to Elfving's embedding problem in classical probability and the divisibility problem of quantum channels.

Item Type:
Journal Article
Journal or Publication Title:
Linear Algebra and its Applications
Additional Information:
This is the author’s version of a work that was accepted for publication in Linear Algebra and its Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Linear Algebra and its Applications, 587, 2020 DOI: 10.1016/j.laa.2019.10.027
Uncontrolled Keywords:
?? complete positivitydivisibilitymarkov chainsmatrix algebrasoperator algebrasquantum informationdiscrete mathematics and combinatoricsalgebra and number theorygeometry and topologynumerical analysis ??
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Deposited On:
20 Nov 2019 11:35
Last Modified:
26 May 2024 01:14