Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 138, Pages 19–49 (Mi into212)  
This article is cited in 7 scientific papers (total in 7 papers)

Algebras of projectors and mutually unbiased bases in dimension 7

I. Yu. Zhdanovskiiab, A. S. Kocherovaa

a Moscow Institute of Physics and Technology
b National Research University "Higher School of Economics" (HSE), Moscow
Full-text PDF (407 kB) Citations (7)
Abstract: We apply methods of the representation theory, combinatorial algebra, and noncommutative geometry to various problems of quantum tomography. We introduce the algebra of projectors that satisfy a certain commutation relation, examine this relation by combinatorial methods, and develop the representation theory of this algebra. We also present a geometrical interpretation of our problem and apply the results obtained to the description of the Petrescu family of mutually unbiased bases in dimension $7$.
Keywords: mutually unbiased bases, orthogonal pairs, commutation relation, algebra of observables.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00113_а
14-01-00416_а
Ministry of Education and Science of the Russian Federation
This work was supported within the State Program of Support of the Leading Universities of the Russian Federation “5-100.” The first author was also partially supported by the Russian Foundation for basic Research (project Nos. 16-01-00113a and 14-01-00416).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 2, Pages 125–157
DOI: https://doi.org/10.1007/s10958-019-04413-8
Bibliographic databases:
Document Type: Article
UDC: 519.248.3, 512.552.8
MSC: 94A40, 16G99
Language: Russian
Citation: I. Yu. Zhdanovskii, A. S. Kocherova, “Algebras of projectors and mutually unbiased bases in dimension 7”, Quantum computing, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 138, VINITI, Moscow, 2017, 19–49; Journal of Mathematical Sciences, 241:2 (2019), 125–157
Citation in format AMSBIB
\Bibitem{ZhdKoc17}
\by I.~Yu.~Zhdanovskii, A.~S.~Kocherova
\paper Algebras of projectors and mutually unbiased bases in dimension~7
\inbook Quantum computing
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 138
\pages 19--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into212}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801249}
\zmath{https://zbmath.org/?q=an:1428.94047}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 2
\pages 125--157
\crossref{https://doi.org/10.1007/s10958-019-04413-8}
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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