Phase operators, phase states and vector phase states for SU3 and SU2, 1

DOI10.1063/1.3620414zbMath1272.81055arXiv1104.4452OpenAlexW3212796224MaRDI QIDQ2849715

Maurice R. Kibler, Mohammed Daoud

Publication date: 24 September 2013

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.4452

zbMATH Keywords

generalized oscillator algebraconstruction of mutually unbiased bases

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Applications of Lie groups to the sciences; explicit representations (22E70) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Numerical methods for discrete and fast Fourier transforms (65T50) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items

A polynomial class of u(2) algebras ⋮ The \(\kappa\)-deformed Boson algebra and parafermion algebra ⋮ Stabilizer codes and equientangled bases from phase states ⋮ Absolutely maximally entangled states from phase states ⋮ \(\kappa\)-deformed photon and Jaynes-Cummings model ⋮ Generalized fermion algebra ⋮ Generalized Grassmann variables for quantum kit (k-level) systems and Barut–Girardello coherent states for su(r + 1) algebras ⋮ Quantum secret sharing protocol using maximally entangled multi-qudit states ⋮ k-uniform maximally mixed states from multi-qudit phase states ⋮ Randomized entangled mixed states from phase states ⋮ Quantum information: a brief overview and some mathematical aspects

Cites Work

• Unnamed Item
• \(\mathrm{SU}(2)\) and \(\mathrm{SU}(1,1)\) approaches to phase operators and temporally stable phase states: Applications to mutually unbiased bases and discrete Fourier transforms
• Vector coherent states from Plancherel's theorem, Clifford algebras and matrix domains
• Some physical appearances of vector coherent states and coherent states related to degenerate Hamiltonians
• Variations on a theme of Heisenberg, Pauli and Weyl
• Phase operators, temporally stable phase states, mutually unbiased bases and exactly solvable quantum systems
• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, the unitary group and the Pauli group
• Coherent states for systems with discrete and continuous spectrum
• Factorization of analytic representations in the unit disc and number-phase statistics of a quantum harmonic oscillator
• Multicomplementary operators via finite Fourier transform
• Quantum phases of a qutrit
• Coherent state realizations of su(n+1) on the n-torus
• A class of vector coherent states defined over matrix domains
• ANGULAR MOMENTUM AND MUTUALLY UNBIASED BASES
• MULTIPARTITE QUANTUM SYSTEMS: PHASES DO MATTER AFTER ALL
• Lie and Jordan Triple Systems