Miscellaneous Applications of Quons

Maurice R. Kibler

Symmetry, integrability and geometry: methods and applications, Tome 3 (2007)

Résumé

This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We motivate why such algebras are interesting for fractional supersymmetric quantum mechanics, angular momentum theory and quantum information. More precisely, quon algebras are used for (i) a realization of a generalized Weyl–Heisenberg algebra from which it is possible to associate a fractional supersymmetric dynamical system, (ii) a polar decomposition of $\mathrm{SU}_2$ and (iii) a construction of mutually unbiased bases in Hilbert spaces of prime dimension. We also briefly discuss (symmetric informationally complete) positive operator valued measures in the spirit of (iii).

Détail

Keywords: quon algebra; $q$-deformed oscillator algebra; fractional supersymmetric quantum mechanics; polar decompostion of $\mathrm{SU}_2$; mutually unbiased bases; positive operator valued measures.

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