Rights statement: 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
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Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Roots of completely positive maps
AU - Bhat, B.V.R.
AU - Hillier, Robin
AU - Mallick, Nirupama
AU - U., Vijaya Kumar
N1 - 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
PY - 2020/2/15
Y1 - 2020/2/15
N2 - 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.
AB - 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.
KW - Complete positivity
KW - Divisibility
KW - Markov chains
KW - Matrix algebras
KW - Operator algebras
KW - Quantum information
U2 - 10.1016/j.laa.2019.10.027
DO - 10.1016/j.laa.2019.10.027
M3 - Journal article
VL - 587
SP - 143
EP - 165
JO - Linear Algebra and its Applications
JF - Linear Algebra and its Applications
SN - 0024-3795
ER -