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

Maurice R Kibler
2009 Journal of Physics A: Mathematical and Theoretical  
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 pairs, generalized Pauli operators and their application to the unitary group and the Pauli group
more » ... e Pauli group naturally arise in this approach.
doi:10.1088/1751-8113/42/35/353001 fatcat:wemtg37fmnapnl4ffn5rbot3ry