2006/01/31 by M. R. Kibler, Maurice Kibler, Michel Planat +1 · 2 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #graph theory and CDMA systems #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1142/s0217979206034303
published as International Journal of Modern Physics B 20 (2006) 1802-1807 · v2: abstract enlarged, a corollary added, acknowledgments added, one reference added, presentation improved; v3: two misprints corrected
openalex publication_date 2006/05/20 · arxiv created 2006/05/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A simple recipe for generating a complete set of mutually unbiased bases in dimension 2j + 1, with 2j integer and 2j + 1 prime, is developed from a single matrix V a acting on a space of constant angular momentum j and defined in terms of the irreducible characters of the cyclic group C 2j + 1 . This recipe yields an (apparently new) compact formula for the vectors spanning the various mutually unbiased bases. In dimension (2j + 1) e , with 2j integer, 2j + 1 prime and e positive integer, the use of direct products of matrices of type V a makes it possible to generate mutually unbiased bases. As two pending results, the matrix V a is used in the derivation of a polar decomposition of SU (2) and of a FFZ algebra.