arXiv 0709.36982007-09-24quant-phmath-phmath.MP

Quons的其他应用

Miscellaneous Applications of Quons

Maurice R. Kibler

备注：: This is a contribution to the Proc. of the 3-rd Microconference "Analytic and Algebraic Methods III"(June 19, 2007, Prague, Czech Republic), published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
发表信息：: SIGMA 3 (2007), 092, 14 pages
DOI：: 10.3842/SIGMA.2007.092

摘要：

本文研究了变形参数是单位根的quon代数或变形振子代数。这些代数在分数阶超对称量子力学、角动量理论和量子信息等方面具有重要的应用价值。更准确地说，quon代数用于（i）实现的广义Weyl-Heisenberg代数，它是可能的，从关联的分数超对称动力系统，（ii）极分解的SU_2和（iii）建设互无偏基的Hilbert空间的素数维。我们还本着（iii）的精神简要讨论了（对称信息完全）正算子值测度。

英文摘要：

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).

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