Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Lecture notes in physics

Quantum Probability Theory and the Foundations of Quantum Mechanics

Jürg Martin Fröhlich, Baptiste Schubnel

Published Jan 1, 2015• 36 citations
Publisher
DOI
10.1007/978-3-662-46422-9_7

Related papers

Quantum Probability and The Foundations of Quantum Theory

Luigi Accardi

Boston studies in the philosophy of science•Jan 1, 1990•3 citations

Foundations of probability and physics--5 : Växjö, Sweden, 24-27 August 2008

Luigi Accardi

This conference was devoted to fundamental questions raised by quantum mechanics, especially in quantum information theory. As has become customary in our series of conference in Vaxjo, we were glad to welcome a fruitful assembly of theoretical physicists, experimentalists, mathematicians and even philosophers interested in the foundations of probability and physics. This conference belongs to the series of Vaxjo conferences in foundations of quantum mechanics (especially probabilistic foundations) combined of two subseries, Foundations of Probability and Physics: 2000, 02, 04, 06, 08, and Quantum Theory: Reconsideration of Foundations: 2001, 03, 05, 07. We also mention the first Vaxjo conference: Bohmian mechanics 2000. This is definitely the longest series of conferences on foundations in the history of quantum mechanics.

AIP eBooks•Jan 1, 2009•0 citations

The foundations of probability and quantum mechanics

Peter Milne

Journal of Philosophical Logic•Apr 1, 1993•3 citations

Implications of quantum theory in the foundations of statistical mechanics

David Wallace

An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.

•Aug 1, 2001•28 citations

Beyond Kolmogorov: Towards a Non-Commutative Measure Theory of Quantum Probability Spaces

Revista, Zen, MATH, 10

This paper explores the limitations of Kolmogorov's measure-theoretic foundation of probability in the context of quantum mechanics and proposes an extension towards a non-commutative framework. We delve into the mathematical structures underlying quantum probability spaces, focusing on operator algebras and their associated states. We analyze the challenges in defining joint probabilities for non-commuting observables and present an overview of alternative approaches based on operator algebras, quantum logic, and non-commutative integration. Furthermore, we investigate the applications of non-commutative measure theory in quantum information theory, quantum field theory, and the foundations of quantum mechanics, highlighting the potential for a more comprehensive understanding of probabilistic phenomena in quantum systems.

•Dec 5, 2025•0 citations

Probability Theory in Quantum Mechanics

L. E. Ballentine

Springer eBooks•Jan 1, 1989•7 citations
This conference was devoted to fundamental questions raised by quantum mechanics, especially in quantum information theory. As has become customary in our series of conference in Vaxjo, we were glad to welcome a fruitful assembly of theoretical physicists, experimentalists, mathematicians and even philosophers interested in the foundations of probability and physics. This conference belongs to the series of Vaxjo conferences in foundations of quantum mechanics (especially probabilistic foundations) combined of two subseries, Foundations of Probability and Physics: 2000, 02, 04, 06, 08, and Quantum Theory: Reconsideration of Foundations: 2001, 03, 05, 07. We also mention the first Vaxjo conference: Bohmian mechanics 2000. This is definitely the longest series of conferences on foundations in the history of quantum mechanics.
An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a theory in its own right; this is necessary if we are to understand statistical-mechanical systems in our own world. Relevant structural and dynamical differences are identified between classical and quantum mechanics (partly through analysis of technical work on quantum chaos by other authors). These imply that quantum mechanics significantly affects a number of foundational questions, including the nature of statistical probability and the direction of time.
This paper explores the limitations of Kolmogorov's measure-theoretic foundation of probability in the context of quantum mechanics and proposes an extension towards a non-commutative framework. We delve into the mathematical structures underlying quantum probability spaces, focusing on operator algebras and their associated states. We analyze the challenges in defining joint probabilities for non-commuting observables and present an overview of alternative approaches based on operator algebras, quantum logic, and non-commutative integration. Furthermore, we investigate the applications of non-commutative measure theory in quantum information theory, quantum field theory, and the foundations of quantum mechanics, highlighting the potential for a more comprehensive understanding of probabilistic phenomena in quantum systems.