Angular Momentum and Mutually Unbiased Bases
نویسنده
چکیده
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 the eigenvectors of the complete set of commuting operators {J2, Ur} and mutually unbiased bases in spaces of constant angular momentum.
منابع مشابه
An angular momentum approach to quadratic Fourier transform , Hadamard matrices , Gauss sums , mutually unbiased bases , unitary group and Pauli group
The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and analysed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl p...
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