TL;DR
This paper explores the applications of quon algebras with roots of unity in fractional supersymmetric quantum mechanics, angular momentum, and quantum information, demonstrating their utility in various quantum theoretical frameworks.
Contribution
It introduces new uses of quon algebras for realizing generalized Weyl-Heisenberg algebras, polar decompositions of SU_2, and constructing mutually unbiased bases in prime-dimensional Hilbert spaces.
Findings
Realization of a generalized Weyl-Heisenberg algebra
Polar decomposition of SU_2 achieved
Construction of mutually unbiased bases in prime dimensions
Abstract
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras 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 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).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.