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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 138, Pages 19–49
(Mi into212)
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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
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.
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
Linking options:
https://www.mathnet.ru/eng/into212 https://www.mathnet.ru/eng/into/v138/p19
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Abstract page: | 544 | Full-text PDF : | 132 | First page: | 17 |
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