Paper Info
Title
New Challenges for Classical and Quantum Probability
Abstract
The discovery that any classical random variable with all moments gives rise to a full quantum theory (that in the Gaussian and Poisson cases coincides with the usual one) implies that a quantum-type formalism will enter into practically all applications of classical probability and statistics. The new challenge consists in finding the classical interpretation, for different types of classical contexts, of typical quantum notions such as entanglement, normal order, equilibrium states, etc. As an example, every classical symmetric random variable has a canonically associated conjugate momentum. In usual quantum mechanics (associated with Gaussian or Poisson classical random variables), the interpretation of the momentum operator was already clear to Heisenberg. How should we interpret the conjugate momentum operator associated with classical random variables outside the Gauss-Poisson class? The Introduction is intended to place in historical perspective the recent developments that are the main object of the present exposition.
Year
DOI
Venue
2022
10.3390/e24101502
ENTROPY
Keywords
DocType
Volume
quantum probability, orthogonal polynomials, quantum decomposition of a classical random variable
Journal
24
Issue
ISSN
Citations 
10
1099-4300
0
PageRank 
References 
Authors
0.34
0
1
Name
Order
Citations
PageRank
Luigi Accardi1116.36