A SU(2) RECIPE FOR MUTUALLY UNBIASED BASES

Author:

KIBLER MAURICE R.1,PLANAT MICHEL2

Affiliation:

1. Institut de Physique Nucléaire de Lyon, IN2P3-CNRS/Université Claude Bernard Lyon 1, 43 bd du 11 novembre 1918, F-69622 Villeurbanne Cedex, France

2. Institut FEMTO-ST, Département LPMO, CNRS/Université de Franche-Comté, 32 avenue de l'Observatoire, F-25044 Besançon Cedex, France

Abstract

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 Va acting on a space of constant angular momentum j and defined in terms of the irreducible characters of the cyclic group C2j + 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 Va makes it possible to generate mutually unbiased bases. As two pending results, the matrix Va is used in the derivation of a polar decomposition of SU (2) and of a FFZ algebra.

Publisher

World Scientific Pub Co Pte Lt

Subject

Condensed Matter Physics,Statistical and Nonlinear Physics

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