Algebras of Projectors and Mutually Unbiased Bases in Dimension 7

Algebras of Projectors and Mutually Unbiased Bases in Dimension 7

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 representat...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) Vol. 241; no. 2; pp. 125 - 157
Main Authors: Zhdanovskiy, I. Yu, Kocherova, A. S.
Format: Journal Article
Language:English
Published: New York Springer US 28-08-2019
Springer
Springer Nature B.V
Subjects:
ALGEBRA
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Combinatorial analysis
Commutation
COMMUTATION RELATIONS
GEOMETRY
Information theory
MATHEMATICAL METHODS AND COMPUTING
Mathematics
Mathematics and Statistics
Projectors
Representations
TOMOGRAPHY
algebra of observables
94A40
orthogonal pairs
mutually unbiased bases
commutation relation
16G99
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Summary: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.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-019-04413-8