Symmetries of finite Heisenberg groups for κ-partite systems

Abstract

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 ℤni, i = 1,…, κ. Their Hilbert spaces are given by κ-fold tensor products of Hilbert spaces of dimensions n1,…, nκ. 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.