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arXiv · 1812.08123

Roots of Completely Positive Maps

B. V. Rajarama Bhat·Robin Hillier·Nirupama Mallick·Vijaya Kumar U
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Abstract

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.

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BibTeXRIS

B. V. Rajarama Bhat, Robin Hillier, Nirupama Mallick, Vijaya Kumar U. 2018-12-19. Roots of Completely Positive Maps. https://doi.org/10.1016/j.laa.2019.10.027

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