Symmetries of the finite Heisenberg group for composite systems

摘要

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, ?)-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.