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

Journal of Physics A Mathematical and General

Entangled states in stochastic mechanics

Nicola Cufaro Petroni, Laura M. Morato

Published Aug 10, 2000• 17 citations
Publisher

Abstract

An axiomatization of the core part of stochastic mechanics (SM) is proposed and this scheme is discussed as a hidden variables theory. We work out in detail an example with entanglement and rigorously prove that SM and quantum mechanics agree in predicting all the observed correlations at different times.
DOI
10.1088/0305-4470/33/33/304

Related papers

Hidden variable theories and quantum nonlocality

A. David. Boozer

We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of quantum mechanics. These example theories clarify some subtle points, which are often misunderstood, regarding what it is that Bell's theorem actually establishes. \n

European Journal of Physics•Feb 9, 2009•2 citations

Local hidden–variable models for entangled quantum states

Remigiusz Augusiak, Maciej Demianowicz, A Acín

While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden--variable models and, therefore, do not violate any Bell inequality. We provide an up to date overview of the existing local hidden--variable models for entangled quantum states, both in the bipartite and multipartite case, and discuss some of the most relevant open questions in this context. Our review covers twenty five years of this line of research since the seminal work by Werner [R. F. Werner, Phys. Rev. A 40, 8 (1989)] providing the first example of an entangled state with a local model, which in turn appeared twenty five years after the seminal work by Bell [J. S. Bell, Physics 1, 195 (1964)], about the impossibility of recovering the predictions of quantum mechanics using a local hidden--variables theory.

arXiv:1405.7321•Journal of Physics A Mathematical and Theoretical•Oct 9, 2014•105 citations

Repeated measurements in stochastic mechanics

Philippe Blanchard, Simon Golin, Maurizio Serva

Stochastic mechanics provides a probabilistic scheme for the description of quantum systems. Grabert, Haaumlnggi, and Talkner, and Nelson have pointed out that its multitime correlations seem to be in disagreement with quantum-mechanical predictions. We show that these difficulties are removed upon a careful analysis of repeated measurements in stochastic mechanics. The wave-packet reduction is naturally described in the stochastic framework, and the predictions for repeated measurements consequently agree in both theories.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 15, 1986•29 citations

A hidden variables model for non-relativistic quantum mechanics in terms of probabilities of particle paths

Emilio Santos

It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory providing an intuitive picture of particle motion. The change of velocity at every time has a probability that depends on the potential over a large region, at a difference with the local action of classical dynamics. Thus the hidden variables theory is non-local like Bohm's, but not deterministic.

arXiv:1603.02215•Mar 7, 2016•0 citations

Entanglement: quantum or classical?

Dilip Paneru, Eliahu Cohen, Robert Fickler +2 more

From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.

arXiv:1911.02201•Reports on Progress in Physics•Apr 1, 2020•84 citations

Entanglement's dynamics from classical stochastic process

Andrei Yu. Khrennikov

Entanglement is still one of the main mysteries of QM. In this note we show that entanglement and its dynamics can be described by classical (so to say “prequantum”) stochastic processes. This construction supports the original Einstein's attempt to reduce entanglement to correlations induced by the preparation procedure.

Europhysics Letters (EPL)•Nov 1, 2009•43 citations
We clarify the meaning of Bell's theorem and its implications for the construction of hidden variable theories by considering an example system consisting of two entangled spin-1/2 particles. Using this example, we present a simplified version of Bell's theorem and describe several hidden variable theories that agree with the predictions of quantum mechanics. These example theories clarify some subtle points, which are often misunderstood, regarding what it is that Bell's theorem actually establishes. \n
While entanglement and violation of Bell inequalities were initially thought to be equivalent quantum phenomena, we now have different examples of entangled states whose correlations can be described by local hidden--variable models and, therefore, do not violate any Bell inequality. We provide an up to date overview of the existing local hidden--variable models for entangled quantum states, both in the bipartite and multipartite case, and discuss some of the most relevant open questions in this context. Our review covers twenty five years of this line of research since the seminal work by Werner [R. F. Werner, Phys. Rev. A 40, 8 (1989)] providing the first example of an entangled state with a local model, which in turn appeared twenty five years after the seminal work by Bell [J. S. Bell, Physics 1, 195 (1964)], about the impossibility of recovering the predictions of quantum mechanics using a local hidden--variables theory.
Stochastic mechanics provides a probabilistic scheme for the description of quantum systems. Grabert, Haaumlnggi, and Talkner, and Nelson have pointed out that its multitime correlations seem to be in disagreement with quantum-mechanical predictions. We show that these difficulties are removed upon a careful analysis of repeated measurements in stochastic mechanics. The wave-packet reduction is naturally described in the stochastic framework, and the predictions for repeated measurements consequently agree in both theories.
It is proved that in non-relativistic quantum mechanics (without spin) the transition probability may be described in terms of particle paths, every path having a (positive) probability. This leads to a stochastic hidden variables theory providing an intuitive picture of particle motion. The change of velocity at every time has a probability that depends on the potential over a large region, at a difference with the local action of classical dynamics. Thus the hidden variables theory is non-local like Bohm's, but not deterministic.
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.