Phase operators, phase states and vector phase states for SU(3) and SU(2,1)

Abstract

This paper focuses on phase operators, phase states and vector phase states for the sl(3) Lie algebra. We introduce a one-parameter generalized oscillator algebra A(k,2) which provides a unified scheme for dealing with su(3) (for k < 0), su(2,1) (for k > 0) and h(4) x h(4) (for k = 0) symmetries. Finite- and infinite-dimensional representations of A(k,2) are constructed for k < 0 and k > 0 or = 0, respectively. Phase operators associated with A(k,2) are defined and temporally stable phase states (as well as vector phase states) are constructed as eigenstates of these operators. Finally, we discuss a relation between quantized phase states and a quadratic discrete Fourier transform and show how to use these states for constructing mutually unbiased bases.

References in corpus (5)

• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems
• Variations on a theme of Heisenberg, Pauli and Weyl
• SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
• SU(3) phase states and finite Fourier transform

Cited by in corpus (5)

• Generalized Weyl-Heisenberg algebra, qudit systems and entanglement measure of symmetric states via spin coherent states
• Generalized fermion algebra
• Generalized Grassmann variables for quantum kit (k-level) systems and Barut-Girardello coherent states for su(r+1) algebras
• SU(3) phase states and finite Fourier transform
• A polynomial class of $u(2)$ algebras