Symmetries of the finite Heisenberg group for composite systems

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.

arXiv commentSubmitted to J. Phys. A: Math. Theor

References in corpus (8)

• Quantum Cryptography
• Security bound of two-bases quantum key-distribution protocols using qudits
• Variations on a theme of Heisenberg, Pauli and Weyl
• Automorphisms of the fine grading of sl(n,C) associated with the generalized Pauli matrices
• Group theoretical construction of mutually unbiased bases in Hilbert spaces of prime dimensions
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• Weak mutually unbiased bases
• Symmetries of finite Heisenberg groups for multipartite systems
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• Clifford group is not a semidirect product in dimensions $N$ divisible by four
• A classification of finite quantum kinematics
• Symmetries of finite Heisenberg groups for k-partite systems
• The Weyl group of the fine grading of $sl(n,\mathbb{C})$ associated with tensor product of generalized Pauli matrices