2022/10/17 by Raphaël Chétrite, Chetrite, Raphael, Frédéric Patras +1
Computer Science · Mathematics · Physics and Astronomy · #Advanced Algebra and Logic #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Random Matrices and Applications
paper · doi:10.48550/arxiv.2210.09264
openalex publication_date 2022/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.