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Modern Physics Letters B

WEAK MEASUREMENTS

J. G. Story, Nicholas W. M. Ritchie, Randall G. Hulet

Published Nov 10, 1991• 11 citations
Publisher

Abstract

A general description of weak measurements is presented. The “weak value” of an operator in pre- and post-selected systems is described both mathematically and using physical arguments. An optical experiment in which a measurement of a weak value has been realized is described. The possible use of pre- and post-selection as a means to amplify and detect weak effects is also discussed.

DOI
10.1142/s0217984991002069

Related papers

Measuring the weak value in an optical experiment

Nicholas W. M. Ritchie

The first experimental realization of a measurement of the weak value of a variable, a concept recently introduced by Aharonov, Albert and Vaidman, is presented. Weak measurements (measurements of a weak value) address the situation in which the separation of the eigenvalues caused by a weakly interacting measurement device is small compared to the width of the distribution of the individual eigenvalues. By appropriate choice of the pre- and post-selected state it is possible that the overlapping eigenvalues will interfere producing a value outside the range of eigenvalues. We demonstrate that the weak value is a practical method of amplifying and resolving the separation between overlapping eigenvalues in an optical experiment proposed by Duck, Stevenson and Sudarshan. In this experiment a birefringent crystal spatially separates two linear polarization components of a Gaussian laser beam by a distance much smaller than the beam waist.

•Jan 1, 1991•0 citations

Weak Measurements

Lev Vaidman A

Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very different for the eigenvalues of the measured operators. The weak values yield novel rich structure of the quantum world. Weak values help explaining peculiar quantum phenomena and finding new effects which might have practical applications.

arXiv:hep-th/9408154•Aug 28, 1994•9 citations

Does the post-selection amplify the information for parameter estimation?

Saki Tanaka, Naoki Yamamoto

It is known that the weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment, implies the possibility to estimate a very small parameter using the weak measurement technique. But does the weak measurement really bring about the increase of information for parameter estimation? This paper provides an answer to this question, in a general situation.

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Anomalous Weak Values Without Post-Selection

Alastair A. Abbott, Ralph Silva, Julian Wechs +2 more

A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.

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Weak value in the wave function of a measuring device

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A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the realization of the weak measurement by the optical polarization and obtain the weak value for any pre- and post-selections. This formula automatically includes the interference effect which is necessary to yields the weak value as an outcome of the weak measurement.

•May 26, 2010•0 citations

Weak value controversy

Lev Vaidman A

Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide useful amplification techniques for precision measurements of small effects in many realistic situations. The statistical nature of weak values is questioned. Although measuring weak values requires an ensemble, it is argued that the weak value, similarly to an eigenvalue, is a property of a single pre- and post-selected quantum system.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

arXiv:1703.08870•Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Oct 2, 2017•91 citations
A general description of weak measurements is presented. The “weak value” of an operator in pre- and post-selected systems is described both mathematically and using physical arguments. An optical experiment in which a measurement of a weak value has been realized is described. The possible use of pre- and post-selection as a means to amplify and detect weak effects is also discussed.
The first experimental realization of a measurement of the weak value of a variable, a concept recently introduced by Aharonov, Albert and Vaidman, is presented. Weak measurements (measurements of a weak value) address the situation in which the separation of the eigenvalues caused by a weakly interacting measurement device is small compared to the width of the distribution of the individual eigenvalues. By appropriate choice of the pre- and post-selected state it is possible that the overlapping eigenvalues will interfere producing a value outside the range of eigenvalues. We demonstrate that the weak value is a practical method of amplifying and resolving the separation between overlapping eigenvalues in an optical experiment proposed by Duck, Stevenson and Sudarshan. In this experiment a birefringent crystal spatially separates two linear polarization components of a Gaussian laser beam by a distance much smaller than the beam waist.
It is known that the weak measurement can significantly amplify the mean of measurement results, sometimes out of the range limited in usual quantum measurement. This fact, as actively demonstrated recently in both theory and experiment, implies the possibility to estimate a very small parameter using the weak measurement technique. But does the weak measurement really bring about the increase of information for parameter estimation? This paper provides an answer to this question, in a general situation.
A weak measurement performed on a pre- and post-selected quantum system can result in an average value that lies outside of the observable's spectrum. This effect, usually referred to as an ``anomalous weak value'', is generally believed to be possible only when a non-trivial post-selection is performed, i.e., when only a particular subset of the data is considered. Here we show, however, that this is not the case in general: in scenarios in which several weak measurements are sequentially performed, an anomalous weak value can be obtained without post-selection, i.e., without discarding any data. We discuss several questions that this raises about the subtle relation between weak values and pointer positions for sequential weak measurements. Finally, we consider some implications of our results for the problem of distinguishing different causal structures.
A simple formula to read out the weak value from the wave function of the measuring device after the postselection with the initial Gaussian profile is proposed. We apply this formula for the weak value to the classical experiment of the realization of the weak measurement by the optical polarization and obtain the weak value for any pre- and post-selections. This formula automatically includes the interference effect which is necessary to yields the weak value as an outcome of the weak measurement.
Recent controversy regarding the meaning and usefulness of weak values is reviewed. It is argued that in spite of recent statistical arguments by Ferrie and Combes, experiments with anomalous weak values provide useful amplification techniques for precision measurements of small effects in many realistic situations. The statistical nature of weak values is questioned. Although measuring weak values requires an ensemble, it is argued that the weak value, similarly to an eigenvalue, is a property of a single pre- and post-selected quantum system.This article is part of the themed issue 'Second quantum revolution: foundational questions'.