2010 Symmetries of the finite Heisenberg group for composite systems

Abstract. Symmetries of the finite Heisenberg group represent an im-portant tool for the study of deeper structure of finite-dimensional quan-tum mechanics. As is well known, these symmetries are properly ex-pressed in terms of certain normalizer. This paper extends previous investigations to composite quantum systems consisting of two subsys-tems — 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. Contents

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