Symmetries of the finite Heisenberg group for composite systems
arXiv:1006.0328 · doi:10.1088/1751-8113/43/37/375302
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.
Submitted to J. Phys. A: Math. Theor
References in corpus (5)
- Security bound of two-bases quantum key-distribution protocols using qudits
- Variations on a theme of Heisenberg, Pauli and Weyl
- Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions
- Feynman's path integral and mutually unbiased bases
- Graded contractions of the Pauli graded sl(3,C)