Algebraic structures underlying quantum independences : Theory and Applications

• URL: http://arxiv.org/abs/2210.09264v1
• Date: Mon, 17 Oct 2022 17:12:04 GMT
• Title: Algebraic structures underlying quantum independences : Theory and Applications
• Authors: Raphael Chetrite, Frederic Patras
• Abstract summary: We reconcile two approaches to quantum probabilities: one physical and coming directly from quantum mechanics, the other more algebraic. We provide a unified picture introducing jointly to several fields of applications, many of which are probably not all familiar. We take the opportunity to present various results obtained recently in the various noncommutative probability theories.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture introducing jointly to several fields of applications, many of which are probably not all familiar (at leat at the same time and in the form we use to present them) to the readers. Lastly, we take the opportunity to present various results obtained recently that use group and bialgebra techniques to handle notions such as cumulants or Wick polynomials in the various noncommutative probability theories.

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