On non-commutativity in quantum theory (I): from classical to quantum
probability
C. Luca. (2018)cite arxiv:1803.04913Comment: 19 pages, 1 figure.
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.
Description
On non-commutativity in quantum theory (I): from classical to quantum
probability
%0 Journal Article
%1 luca2018noncommutativity
%A Luca, Curcuraci
%D 2018
%K quantum
%T On non-commutativity in quantum theory (I): from classical to quantum
probability
%U http://arxiv.org/abs/1803.04913
%X 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.
@article{luca2018noncommutativity,
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.},
added-at = {2018-03-15T16:01:52.000+0100},
author = {Luca, Curcuraci},
biburl = {https://www.bibsonomy.org/bibtex/25d0f7b35fa5097afba667d699600e243/claired},
description = {On non-commutativity in quantum theory (I): from classical to quantum
probability},
interhash = {e0b530cfbc0740e2207f8ec868d2f277},
intrahash = {5d0f7b35fa5097afba667d699600e243},
keywords = {quantum},
note = {cite arxiv:1803.04913Comment: 19 pages, 1 figure},
timestamp = {2018-03-15T16:01:52.000+0100},
title = {On non-commutativity in quantum theory (I): from classical to quantum
probability},
url = {http://arxiv.org/abs/1803.04913},
year = 2018
}