Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an $N^{2}$-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase-space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.Comment: 16 pages; 3 figure

A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials

We discuss some results from q-series that can account for the foundations for the introduction of orthogonal polynomials on the circle and on the line, namely the Rogers-Szegö and Stieltjes-Wigert polynomials. These polynomials are explicitly written and their orthogonality is verified. Explicit realizations of the raising and lowering operators for these polynomials are introduced in analogy to those of the Hermite polynomials that are shown to obey the q-commutation relations associated with the q-deformed harmonic oscillator.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

On the structure of quantum phase space

The space of labels characterizing the elements of Schwinger's basis for unitary quantum operators is endowed with a structure of symplectic type. This structure is embodied in a certain algebraic cocycle, whose main features are inherited by the symplectic form of classical phase space. In consequence, the label space may be taken as the quantum phase space: It plays, in the quantum case, the same role played by phase space in classical mechanics, some differences coming inevitably from its nonlinear character. © 1990 American Institute of Physics

Discrete and canonical quantum variables

A connection betweend discrete, Cartesian and angular quantum variables is obtained and discussed.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES