An angular momentum approach to quadratic Fourier transform , Hadamard matrices , Gauss sums , mutually unbiased bases , unitary group and Pauli group

@inproceedings{Kibler2009AnAM,
  title={An angular momentum approach to quadratic Fourier transform , Hadamard matrices , Gauss sums , mutually unbiased bases , unitary group and Pauli group},
  author={Maurice R. Kibler},
  year={2009}
}
The construction of unitary operator bases in a finite-dimen sional 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 tr ansforms, Hadamard matrices and generalized Gauss sums. Weyl p airs, generalized Pauli operators and their application to the unitary group and the Pauli group… CONTINUE READING