Email this article Algebras of Projectors and Mutually Unbiased Bases in Dimension 7
- Authors: Zhdanovskiy I.Y.1,2, Kocherova A.S.1
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Affiliations:
- Moscow Institute of Physics and Technology (State University)
- National Research University “High School of Economics, Laboratory of Algebraic Geometry
- Issue: Vol 241, No 2 (2019)
- Pages: 125-157
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/242868
- DOI: https://doi.org/10.1007/s10958-019-04413-8
- ID: 242868
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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.
About the authors
I. Yu. Zhdanovskiy
Moscow Institute of Physics and Technology (State University); National Research University “High School of Economics, Laboratory of Algebraic Geometry
Author for correspondence.
Email: ijdanov@mail.ru
Russian Federation, Moscow; Moscow
A. S. Kocherova
Moscow Institute of Physics and Technology (State University)
Email: ijdanov@mail.ru
Russian Federation, Moscow
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