Symmetries of the finite Heisenberg group for composite systems

Details Symmetries of the finite Heisenberg group for composite systems Symmetries of the finite Heisenberg group for composite systems

2010-06-02

arxiv.org/abs/1006.0328v1

J. Phys. A: Math. Theor. 43 (2010) 375302 (15pp)

Physics

Quantum Physics

Submitted to J. Phys. A: Math. Theor

Scientific paper

10.1088/1751-8113/43/37/375302

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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