Topological decompositions of the Pauli group and their influence on dynamical systems

Abstract

In the present paper we show that it is possible to obtain the well known Pauli group $P=⟨X,Y,Z|X^2=Y^2=Z^2=1,(YZ{)}^4=(ZX{)}^4=(XY{)}^4=1⟩$ of order $16$ as an appropriate quotient group of two distinct spaces of orbits of the three dimensional sphere $S^3$. The first of these spaces of orbits is realized via an action of the quaternion group $Q_8$ on $S^3$; the second one via an action of the cyclic group of order four $\mathbb{Z}(4)$ on $S^3$. We deduce a result of decomposition of $P$ of topological nature and then we find, in connection with the theory of pseudo-fermions, a possible physical interpretation of this decomposition.

arXiv commentin press in "Mathematical Physics, Analysis and Geometry"

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Cited by in corpus (3)

• On the Pauli group on 2-qubits in dynamical systems with pseudofermions
• Polyadic sigma matrices
• On the subdirect product of graph bundles