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

Weak value as an indicator of back-action

Riuji Mochizuki

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

In this study we critically examine some important papers on weak measurement and weak values. We find some insufficiency and mistakes in these papers, and we demonstrate that the real parts of weak values pro-vide the back-action to the post-selection, which is caused by weak mea-surement. Two examples, a counterfactual statement of Hardy’s paradox and experiments that determine the average trajectory of photons passing through double slits, are investigated from our view point. PACS numbers: 03.65.Ta, 03.65.Ud, 03.65.Ca 1

Related papers

Weak value as an indicator of back-action

Riuji Mochizuki

In this study we critically examine some important papers on weak measurement and weak values. We find some insufficiency and mistakes in these papers, and we demonstrate that the real parts of weak values provide the back-action to the post-selection, which is caused by weak measurement. Two examples, a counterfactual statement of Hardy's paradox and experiments that determine the average trajectory of photons passing through double slits, are investigated from our point of view.

arXiv:1312.3036•Progress of Theoretical and Experimental Physics•Apr 1, 2014•2 citations

Quantum logic and weak values

Riuji Mochizuki

In this study, we study weak values from a quantum-logical viewpoint. In addition, we examine the validity of the counterfactual statements of Hardy's paradox, which are based on weak values, and we show that these statements have not been validated. It is also shown that strange weak values may only appear if they are not (conditional) probabilities. PACS numbers: 03.65.Ta, 03.65.Ud, 03.65.Ca

arXiv:1302.6003•Feb 25, 2013•0 citations

What Is a Quantum-Mechanical “Weak Value” the Value of?

B. E. Y. Svensson

A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes ( e.g. , the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.

arXiv:1301.4328•Foundations of Physics•Sep 4, 2013•27 citations

The real and imaginary parts of a weak value appearing as back-actions via a post-selection

Kazuhiro Yokota

In a weak measurement the real and imaginary parts of a weak value participate in the shifts of the complementary variables of a pointer. While the real part represents the value of an observable in the limit of zero measurement strength, the imaginary one is regarded as the back-action due to the measurement with a post-selection, which has an influence on the post-selection probability. In this paper I give a case in which a real part could also appear as such a back-action in a post-selection probability on an equal footing with an imaginary one. It is also shown that both of the real and imaginary parts can be inferred by observing the probability in practice, which has an advantage that an additional system of a pointer is not needed.

arXiv:1909.04806•Sep 11, 2019•1 citation

Experimental Joint Weak Measurement on a Photon Pair as a Probe of Hardy’s Paradox

Jeff S. Lundeen, Aephraim M. Steinberg

It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.

arXiv:0810.4229•Physical Review Letters•Jan 14, 2009•368 citations

Observing the Weak Value through Quantum Interference

森, 琢也

In quantum mechanics, it is well known that counterfactual arguments sometimes lead to paradoxes, which implies that our classical intuition is not always reliable.However, it has been pointed out by several authors that the weak value, which was introduced by Aharonov et al. in 1988, may be useful to comprehend quantum mechanics intuitively.Another extraordinary aspect of the weak value is its amplification, which has been exploited for precision measurement.Nevertheless, the physical meaning of the weak value is still obscure due to its complexity of the value and the very fact of the amplification.In this thesis, by considering various situations of quantum interference, we attempt to provide a possible interpretation of the weak value.We find, on one hand, that the imaginary part of the weak value is relevant to the wave nature.On the other hand, in the double-slit experiment the particle nature can be seen in the real part of the position weak value.This property for the real part does not hold for more general cases such as the multiple (more than two) slit experiment.The position weak value, nevertheless, can be interpreted as the average of the classical trajectories based on a complex probability.We also investigate the possibility of knowing which path the particle takes in the multiple-slit experiment without destroying the interference fringes.We show that, because of the statistical nature of the weak value, obtaining the which-path information and the interference pattern is compatible with complementarity.Our study suggests that the weak value is a reasonable physical quantity.

•Mar 24, 2015•0 citations
In this study we critically examine some important papers on weak measurement and weak values. We find some insufficiency and mistakes in these papers, and we demonstrate that the real parts of weak values pro-vide the back-action to the post-selection, which is caused by weak mea-surement. Two examples, a counterfactual statement of Hardy’s paradox and experiments that determine the average trajectory of photons passing through double slits, are investigated from our view point. PACS numbers: 03.65.Ta, 03.65.Ud, 03.65.Ca 1
A so called “weak value” of an observable in quantum mechanics (QM) may be obtained in a weak measurement + post-selection procedure on the QM system under study. Applied to number operators, it has been invoked in revisiting some QM paradoxes ( e.g. , the so called Three-Box Paradox and Hardy’s Paradox). This requires the weak value to be interpreted as a bona fide property of the system considered, a par with entities like operator mean values and eigenvalues. I question such an interpretation; it has no support in the basic axioms of quantum mechanics and it leads to unreasonable results in concrete situations.
In a weak measurement the real and imaginary parts of a weak value participate in the shifts of the complementary variables of a pointer. While the real part represents the value of an observable in the limit of zero measurement strength, the imaginary one is regarded as the back-action due to the measurement with a post-selection, which has an influence on the post-selection probability. In this paper I give a case in which a real part could also appear as such a back-action in a post-selection probability on an equal footing with an imaginary one. It is also shown that both of the real and imaginary parts can be inferred by observing the probability in practice, which has an advantage that an additional system of a pointer is not needed.
It has been proposed that the ability to perform joint weak measurements on postselected systems would allow us to study quantum paradoxes. These measurements can investigate the history of those particles that contribute to the paradoxical outcome. Here we experimentally perform weak measurements of joint (i.e., nonlocal) observables. In an implementation of Hardy's paradox, we weakly measure the locations of two photons, the subject of the conflicting statements behind the paradox. Remarkably, the resulting weak probabilities verify all of these statements but, at the same time, resolve the paradox.
In quantum mechanics, it is well known that counterfactual arguments sometimes lead to paradoxes, which implies that our classical intuition is not always reliable.However, it has been pointed out by several authors that the weak value, which was introduced by Aharonov et al. in 1988, may be useful to comprehend quantum mechanics intuitively.Another extraordinary aspect of the weak value is its amplification, which has been exploited for precision measurement.Nevertheless, the physical meaning of the weak value is still obscure due to its complexity of the value and the very fact of the amplification.In this thesis, by considering various situations of quantum interference, we attempt to provide a possible interpretation of the weak value.We find, on one hand, that the imaginary part of the weak value is relevant to the wave nature.On the other hand, in the double-slit experiment the particle nature can be seen in the real part of the position weak value.This property for the real part does not hold for more general cases such as the multiple (more than two) slit experiment.The position weak value, nevertheless, can be interpreted as the average of the classical trajectories based on a complex probability.We also investigate the possibility of knowing which path the particle takes in the multiple-slit experiment without destroying the interference fringes.We show that, because of the statistical nature of the weak value, obtaining the which-path information and the interference pattern is compatible with complementarity.Our study suggests that the weak value is a reasonable physical quantity.