A SU(2) recipe for mutually unbiased bases

M. Kibler (1) , M. Planat (2)

1 IPNL - Institut de Physique Nucléaire de Lyon
2 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

A simple recipe for generating a complete set of mutually unbiased bases in dimension (2j+1)**e, with 2j + 1 prime and e positive integer, is developed from a single matrix acting on a space of constant angular momentum j and defined in terms of the irreducible characters of the cyclic group C(2j+1). As two pending results, this matrix is used in the derivation of a polar decomposition of SU(2) and of a FFZ algebra.

Mots clés: angular momentum; Lie algebra; polar decomposition; deformations; FFZ algebra

Domaines: Physique mathématique [math-ph]; Physique Quantique [quant-ph]

M. Kibler, M. Planat. A SU(2) recipe for mutually unbiased bases. International Journal of Modern Physics B, 2006, 20, pp.1802-1807. ⟨10.1142/S0217979206034303⟩. ⟨in2p3-00025391v3⟩