Symmetries of finite Heisenberg groups for k-partite systems
| Authors | |
|---|---|
| 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 | |
| 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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