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 in the wave function of a measuring device

Kouji Nakamura

Published May 26, 2010• 0 citations
OpenAlex

Abstract

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.

Related papers

Weak Value in Wave Function of Detector

Kouji Nakamura

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.

arXiv:1005.4720•Journal of the Physical Society of Japan•Dec 10, 2010•0 citations

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

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

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.

Modern Physics Letters B•Nov 10, 1991•11 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

On the connection between weak measurement in quantum physics and analytic phase-retrieval in classical wave optics

Nobuharu Nakajima

The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being measured. Consideration of the phase is important to clarify its physical interpretation. In classical wave optics, there has long been studies on methods of measuring or retrieving the phase of a wave function. We here present that one of those methods, the analytic phase retrieval based on the properties of entire functions, has a close connection with weak measurements in quantum physics. We explain such a connection for two emblematic optical weak-measurements that have the same mathematical formalism as quantum systems: one is a system for weak measurements of polarized light displacement in a birefringent crystal, and the other is a system for the direct measurement of a wave function by weakly coupling it to a pointer. In those two systems, we show that the pre- and post-selection of polarized light provides a filtering effect similar to that utilized in the analytic phase retrieval.

arXiv:2312.15597•Dec 25, 2023•0 citations

On the Two-State Vector Reformulation of Quantum Mechanics

Yakir Aharonov, Lev Vaidman A

A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first pre-selected by the initial measurement and the second post-selected by the final measurement describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measuring procedure that fulfills certain requirements of “weakness”. We call it weak measurement . Physical meaning and underlying mathematical structure of weak measurements are explored.

Physica Scripta•Jan 1, 1998•19 citations
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.
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.
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.
The physical interpretation of weak measurements has been the subject of much debate. It is known that anomalous phenomena and results that appear in weak measurements are essentially related to the phase of the quantum system being measured. Consideration of the phase is important to clarify its physical interpretation. In classical wave optics, there has long been studies on methods of measuring or retrieving the phase of a wave function. We here present that one of those methods, the analytic phase retrieval based on the properties of entire functions, has a close connection with weak measurements in quantum physics. We explain such a connection for two emblematic optical weak-measurements that have the same mathematical formalism as quantum systems: one is a system for weak measurements of polarized light displacement in a birefringent crystal, and the other is a system for the direct measurement of a wave function by weakly coupling it to a pointer. In those two systems, we show that the pre- and post-selection of polarized light provides a filtering effect similar to that utilized in the analytic phase retrieval.
A description of quantum systems at the time interval between two successive measurements is presented. Two wave functions, the first pre-selected by the initial measurement and the second post-selected by the final measurement describe quantum systems at a single time. It is shown how this approach leads to a new concept: a weak value of an observable. Weak values represent novel characteristics of quantum systems between two measurements. They are outcomes of a standard measuring procedure that fulfills certain requirements of “weakness”. We call it weak measurement . Physical meaning and underlying mathematical structure of weak measurements are explored.