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Quantum Physics

Title: On non-commutativity in quantum theory (I): from classical to quantum probability

Abstract: A central feature of quantum mechanics is the non-commutativity of operators used to describe physical observables. In this article, we present a critical analysis on the role of non-commutativity in quantum theory, focusing on its consequences in the probabilistic description. Typically, a random phenomenon is described using the measure-theoretic formulation of probability theory. Such a description can also be done using algebraic methods, which are capable to deal with non-commutative random variables (like in quantum mechanics). Here we propose a method to construct a non-commutative probability theory starting from an ordinary measure-theoretic description of probability. This will be done using the entropic uncertainty relations between random variables, in order to evaluate the presence of non-commutativity in their algebraic description.
Comments: 19 pages, 1 figure
Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Probability (math.PR)
Cite as: arXiv:1803.04913 [quant-ph]
  (or arXiv:1803.04913v2 [quant-ph] for this version)

Submission history

From: Luca Curcuraci [view email]
[v1] Tue, 13 Mar 2018 16:15:37 GMT (57kb,D)
[v2] Fri, 16 Mar 2018 20:34:38 GMT (57kb,D)