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Mat. Sb., 2019, Volume 210, Number 7, Pages 21–93 (Mi msb9074)  

This article is cited in 1 scientific paper (total in 1 paper)

Quantum system structures of quantum spaces and entanglement breaking maps

A. A. Dosi

Mathematics Research Group, Middle East Technical University, Northern Cyprus Campus, Güzelyurt, Turkey

Abstract: This paper is devoted to the classification of quantum systems among the quantum spaces. In the normed case we obtain a complete solution to the problem when an operator space turns out to be an operator system. The min and max quantizations of a local order are described in terms of the min and max envelopes of the related state spaces. Finally, we characterize min-max-completely positive maps between Archimedean order unit spaces and investigate entanglement breaking maps in the general setting of quantum systems.
Bibliography: 34 titles.

Keywords: quantum cone, quantum ball, operator systems, quantum systems, entanglement breaking mapping.

DOI: https://doi.org/10.4213/sm9074

Full text: PDF file (1119 kB)
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English version:
Sbornik: Mathematics, 2019, 210:7, 928–993

Bibliographic databases:

UDC: 517.986.242+517.982.354
MSC: Primary 46L07; Secondary 46B40, 47L25
Received: 27.01.2018 and 28.07.2018

Citation: A. A. Dosi, “Quantum system structures of quantum spaces and entanglement breaking maps”, Mat. Sb., 210:7 (2019), 21–93; Sb. Math., 210:7 (2019), 928–993

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm9074
  • http://mi.mathnet.ru/eng/msb/v210/i7/p21

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Asadi M.B., Hassanpour-Yakhdani Z., Shamloo S., “A Locally Convex Version of Kadison'S Representation Theorem”, Positivity  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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