Symmetries of finite Heisenberg groups for k-partite systems

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Authors

KORBELÁŘ Miroslav TOLAR Jiří

Year of publication 2012
Type Article in Proceedings
Conference 7th International Conference on Quantum Theory and Symmetries (QTS7), 7–13 August 2011, Prague, Czech Republic
MU Faculty or unit

Faculty of Science

Citation
Web http://iopscience.iop.org/1742-6596/343/1/012122
Doi http://dx.doi.org/10.1088/1742-6596/343/1/012122
Field General mathematics
Keywords mutually unbiased bases; quantum-mechanics; hilbert-space; construction
Description Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems comprised of k subsystems which are described with position and momentum variables in Z(ni) i - 1, ..., k. Their Hilbert spaces are given by k-fold tensor products of Hilbert spaces of dimensions n(1), ..., n(k). Symmetry group of the corresponding finite Heisenberg group is given by the quotient group of a certain normalizer. We provide the description of the symmetry groups for arbitrary multipartite cases. The new class of symmetry groups represents very specific generalization of finite symplectic groups over modular rings.
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