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

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Comment on "Repeated measurements in stochastic mechanics"

M. S. Wang, Wei‐Kuang Liang

Published Aug 15, 1993• 15 citations
Publisher

Abstract

An example is given to show explicitly that the quantum-mechanical multitime correlations, in general, do not agree with the stochastic-mechanical multitime correlations with the wave function reduction taken into account. This result contradicts the previous assertion made by Blanchard, Golin, and Serva.
DOI
10.1103/physrevd.48.1875

Related papers

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

On the nonoccurrence of two paradoxes in the measurement scheme of stochastic quantum mechanics

Franklin E. Schroeck

Foundations of Physics•Mar 1, 1985•12 citations

Reply to ‘‘Comment on ‘Repeated measurements in stochastic mechanics’ ’’

Philippe Blanchard, Maurizio Serva

In a previous paper we showed that predictions about the results of repeated measurements coincide in quantum and stochastic mechanics when wave-packet collapse is taken into acocunt. Our result removed some apparent paradoxes pointed out by Grabert, H\"anggi, Talkner, and Nelson. Recently Wang and Liang argued that our analysis was incorrect and they produced an explicit counterexample in order to confute our results. We think that their comment is due to a misunderstanding of our paper. For this reason we discuss here, in more detail, the controversial point of our work, concerning the regularization of the quantum-mechanical propagator. After stating more clearly our point, we show that the criticism of Wang and Liang is supported by an improper treatment of the divergences in their counterexample.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Mar 15, 1995•2 citations

Multitime correlation functions in nonclassical stochastic processes

F. Krumm, Jan Sperling, W. Vogel

A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent $P$ functional that generalizes the Glauber-Sudarshan $P$ function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.

arXiv:1603.09555•Physical Review A•Jun 27, 2016•13 citations

Does the phenomenon of `reduction of the wave function' exist in measurements in quantum mechanics?

Аркадий Исаакович Липкин

Physics-Uspekhi•Apr 30, 2001•10 citations

COMMENT ON REPEATED MEASUREMENTS IN STOCHASTIC MECHANICS - REPLY

Blanchard, Philippe, Maurizio Serva

•Jan 1, 1995•1 citation
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.
In a previous paper we showed that predictions about the results of repeated measurements coincide in quantum and stochastic mechanics when wave-packet collapse is taken into acocunt. Our result removed some apparent paradoxes pointed out by Grabert, H\"anggi, Talkner, and Nelson. Recently Wang and Liang argued that our analysis was incorrect and they produced an explicit counterexample in order to confute our results. We think that their comment is due to a misunderstanding of our paper. For this reason we discuss here, in more detail, the controversial point of our work, concerning the regularization of the quantum-mechanical propagator. After stating more clearly our point, we show that the criticism of Wang and Liang is supported by an improper treatment of the divergences in their counterexample.
A general method is introduced for verifying multitime quantum correlations through the characteristic function of the time-dependent PPP functional that generalizes the Glauber-Sudarshan PPP function. Quantum correlation criteria are derived which identify quantum effects for an arbitrary number of points in time. The Magnus expansion is used to visualize the impact of the required time ordering, which becomes crucial in situations when the interaction problem is explicitly time dependent. We show that the latter affects the multi-time-characteristic function and, therefore, the temporal evolution of the nonclassicality. As an example, we apply our technique to an optical parametric process with a frequency mismatch. The resulting two-time-characteristic function yields full insight into the two-time quantum correlation properties of such a system.