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arXiv · 1006.0328

Symmetries of the finite Heisenberg group for composite systems

M. Korbelar·J. Tolar
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Abstract

Symmetries of the finite Heisenberg group represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. As is well known, these symmetries are properly expressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsystems - qudits - with arbitrary dimensions n and m. In this paper we present detailed descriptions - in the group of inner automorphisms of GL(nm,C) - of the normalizer of the Abelian subgroup generated by tensor products of generalized Pauli matrices of orders n and m. The symmetry group is then given by the quotient group of the normalizer.

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M. Korbelar, J. Tolar. 2010-06-02. Symmetries of the finite Heisenberg group for composite systems. https://doi.org/10.1088/1751-8113/43/37/375302

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