On Pauli pairs

Möbius Pairs of Simplices and Commuting Pauli Operators

There exists a large class of groups of operators acting on Hilbert spaces, where commutativity of group elements can be expressed in the geometric language of symplectic polar spaces embedded in the projective spaces PG(n, p), n being odd and p a prime. Here, we present a result about commuting and non-commuting group elements based on the existence of socalled Möbius pairs of n-simplices, i. ...

On the Pauli graphs on N-qudits

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding Pauli graph are embodied in the geometry of the generalized q...

On the zero modes of Pauli operators

ON RELATIVE CENTRAL EXTENSIONS AND COVERING PAIRS

Let (G;N) be a pair of groups. In this article, first we con-struct a relative central extension for the pair (G;N) such that specialtypes of covering pair of (G;N) are homomorphic image of it. Second, weshow that every perfect pair admits at least one covering pair. Finally,among extending some properties of perfect groups to perfect pairs, wecharacterize covering pairs of a perfect pair (G;N)...

On the Heisenberg-pauli-weyl Inequality

In 1927, W. Heisenberg demonstrated the impossibility of specifying simultaneously the position and the momentum of an electron within an atom.The following result named, Heisenberg inequality, is not actually due to Heisenberg. In 1928, according to H. Weyl this result is due to W. Pauli.The said inequality states, as follows: Assume thatf : R → C is a complex valued function of a random real ...