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Symmetries of the finite Heisenberg group for composite systems. (English) Zbl 1198.81062
Summary: Symmetries of the finite Heisenberg group represent an important tool for the study of the deeper structure of finite-dimensional quantum mechanics. As it is well known, these symmetries are properly expressed in terms of a 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.
MSC:
81P45Quantum information, communication, networks
81Q05Closed and approximate solutions to quantum-mechanical equations
81R05Representations of finite-dimensional groups and algebras in quantum theory
81R15Operator algebra methods (quantum theory)