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Mat. Sb., 2013, Volume 204, Number 8, Pages 137–160 (Mi msb8156)  

This article is cited in 4 scientific papers (total in 4 papers)

Reversibility conditions for quantum channels and their applications

M. E. Shirokov

Steklov Mathematical Institute of the Russian Academy of Sciences

Abstract: Conditions for a quantum channel (noncommutative Markov operator) to be reversible with respect to complete families of quantum states with bounded rank are obtained. A description of all quantum channels reversible with respect to a given (orthogonal or nonorthogonal) complete family of pure states is given. Some applications in quantum information theory are considered.
Bibliography: 20 titles.

Keywords: quantum states, quantum channels, relative entropy, $\chi$-quantity of ensemble of quantum states.

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Russian Foundation for Basic Research 12-01-00319-а
13-01-00295а


DOI: https://doi.org/10.4213/sm8156

Full text: PDF file (672 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2013, 204:8, 1215–1237

Bibliographic databases:

UDC: 519.248.3
MSC: Primary 81P45, 81P68; Secondary 46L60, 46N50
Received: 18.07.2012 and 18.03.2013

Citation: M. E. Shirokov, “Reversibility conditions for quantum channels and their applications”, Mat. Sb., 204:8 (2013), 137–160; Sb. Math., 204:8 (2013), 1215–1237

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  • https://doi.org/10.4213/sm8156
  • http://mi.mathnet.ru/eng/msb/v204/i8/p137

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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. Shirokov M.E., “Reversibility of a quantum channel: general conditions and their applications to bosonic linear channels”, J. Math. Phys., 54:11 (2013), 112201, 19 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. M. E. Shirokov, “Criteria for equality in two entropic inequalities”, Sb. Math., 205:7 (2014), 1045–1068  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. P. Sinkovicz, T. Kiss, J. K. Asboth, “Generalized Kac lemma for recurrence time in iterated open quantum systems”, Phys. Rev. A, 93:5 (2016), 050101  crossref  isi  scopus
    4. M. M. Wilde, H. Qi, “Energy-constrained private and quantum capacities of quantum channels”, IEEE Trans. Inf. Theory, 64:12 (2018), 7802–7827  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник Sbornik: Mathematics (from 1967)
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