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Journal of Physics A Mathematical and Theoretical 42 (2009) 353001
An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, unitary group and Pauli group
Maurice Robert Kibler1

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 naturally arise in this approach.
1 :  IPNL - Institut de Physique Nucléaire de Lyon
Physique/Physique Quantique
finite quantum mechanics – angular momentum – Weyl pairs – generalized Pauli operators – quadratic Fourier transform – Hadamard matrices – Gauss sums – mutually unbiased bases – cyclic group – unitary group – Heisenberg-Weyl group – Pauli group
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