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  • RootUCP190107

    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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Roots of completely positive maps

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Roots of completely positive maps. / Bhat, B.V.R.; Hillier, Robin; Mallick, Nirupama et al.
In: Linear Algebra and its Applications, Vol. 587, 15.02.2020, p. 143-165.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Bhat, BVR, Hillier, R, Mallick, N & U., VK 2020, 'Roots of completely positive maps', Linear Algebra and its Applications, vol. 587, pp. 143-165. https://doi.org/10.1016/j.laa.2019.10.027

APA

Bhat, B. V. R., Hillier, R., Mallick, N., & U., V. K. (2020). Roots of completely positive maps. Linear Algebra and its Applications, 587, 143-165. https://doi.org/10.1016/j.laa.2019.10.027

Vancouver

Bhat BVR, Hillier R, Mallick N, U. VK. Roots of completely positive maps. Linear Algebra and its Applications. 2020 Feb 15;587:143-165. Epub 2019 Oct 31. doi: 10.1016/j.laa.2019.10.027

Author

Bhat, B.V.R. ; Hillier, Robin ; Mallick, Nirupama et al. / Roots of completely positive maps. In: Linear Algebra and its Applications. 2020 ; Vol. 587. pp. 143-165.

Bibtex

@article{58439ba1ddf64f859165e195576ae633,
title = "Roots of completely positive maps",
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.",
keywords = "Complete positivity, Divisibility, Markov chains, Matrix algebras, Operator algebras, Quantum information",
author = "B.V.R. Bhat and Robin Hillier and Nirupama Mallick and U., {Vijaya Kumar}",
note = "This is the author{\textquoteright}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",
year = "2020",
month = feb,
day = "15",
doi = "10.1016/j.laa.2019.10.027",
language = "English",
volume = "587",
pages = "143--165",
journal = "Linear Algebra and its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",

}

RIS

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 -