Roots of completely positive maps

Authors

B. V.Rajarama Bhat, Indian Statistical Institute Bangalore
Robin Hillier, Department of Mathematics and Statistics, Lancaster University
Nirupama Mallick, Institute of Mathematical Sciences India
Vijaya Kumar U., Indian Statistical Institute Bangalore

Article Type

Research Article

Publication Title

Linear Algebra and Its Applications

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.

First Page

143

Last Page

165

DOI

10.1016/j.laa.2019.10.027

Publication Date

2-15-2020

Comments

Open Access, Green

Recommended Citation

Bhat, B. V.Rajarama; Hillier, Robin; Mallick, Nirupama; and U., Vijaya Kumar, "Roots of completely positive maps" (2020). Journal Articles. 392.
https://digitalcommons.isical.ac.in/journal-articles/392