A range-kernal orthogonality property is established for the elementary operators (X) = ∑n i=1AiXBi and ∗(X) = ∑n i=1A ∗ i XB ∗ i , where A = (A1,A2, . . . ,An) and B = (B1,B2, . . . ,Bn) are n-tuples of mutually commuting scalar operators (in the sense of Dunford) in the algebra B(H) of operators on a Hilbert space H . It is proved that the operator satisfies Weyl’s theorem in the case in whic...

The Lie algebra of the group SU2 is constructed from two deformed oscillator algebras for which the deformation parameter is a root of unity. This leads to an unusual quantization scheme, the {J2, Ur} scheme, an alternative to the familiar {J2, Jz} quantization scheme corresponding to common eigenvectors of the Casimir operator J and the Cartan operator Jz. A connection is established between t...

In this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid G(n). Also we show that G(n) contains commuting regular subsemigroup and give a necessary and sufficient condition for the groupoid G(n) to be commuting regular.

Abstract We define a “nit” as a radix n measure of quantum information which is based on state partitions associated with the outcomes of n-ary observables and which, for n > 2, is fundamentally irreducible to a binary coding. Properties of this measure for entangled many-particle states are discussed. k particles specify k nits in such a way that k mutually commuting measurements of observable...

Using a similarity transformation that maps the Calogero model into N decoupled quantum harmonic oscillators, we construct a set of mutually commuting conserved operators of the model and their simultaneous eigenfunctions. The simultaneous eigenfunction is a deformation of the symmetrized number state (bosonic state) and forms an orthogonal basis of the Hilbert (Fock) space of the model. This o...

We define a measure of quantum information which is based on state partitions. Properties of this measure for entangled many-particle states are discussed. k particles specify k “nits” in such a way that k mutually commuting measurements of n-ary observables are necessary to determine the information. PACS numbers: 03.65.Ta,03.67.-a

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...