Angular Momentum and Mutually Unbiased Bases

Abstract

The Lie algebra of the group SU(2) 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 J2 and the Cartan operator Jz. A connection is established between the eigenvectors of the complete set of commuting operators {J2,Ur} and mutually unbiased bases in spaces of constant angular momentum.

To be published in International Journal of Modern Physics B

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• An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
• A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
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• Variations on a theme of Heisenberg, Pauli and Weyl
• Phase operators, phase states and vector phase states for SU(3) and SU(2,1)
• SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
• Miscellaneous Applications of Quons
• Generalized spin bases for quantum chemistry and quantum information
• Matrix reduction and Lagrangian submodules
• Bases for spin systems and qudits from angular momentum theory
• Bases for qudits from a nonstandard approach to SU(2)
• Harmonic analysis on a galois field and its subfields