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

arXiv:1205.0619 · Physical Review A

Weak measurement with orthogonal preselection and postselection

Shengshi Pang, Shengjun Wu, Zeng‐Bing Chen

Published Aug 17, 2012• 30 citations
arXivHTMLPDF

Abstract

Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the preselection and the postselection should not be too small generally. In this work, we study the weak measurement on a qubit system with exactly or asymptotically orthogonal pre- and postselections. We shall establish a general rigorous framework for the weak measurement beyond the weak value formalism, and obtain the average output of a weak measurement when the pre- and postselections are exactly orthogonal. We shall also study the asymptotic behavior of a weak measurement in the limiting process that the pre- and postselections tend to be orthogonal.

DOI
10.1103/physreva.86.022112

Related papers

Weak measurements beyond the Aharonov-Albert-Vaidman formalism

Shengjun Wu, Yang Li

We extend the idea of weak measurements to the general case, provide a complete treatment, and obtain results for both the regime when the preselected and postselected states (PPS) are almost orthogonal and the regime when they are exactly orthogonal. We surprisingly find that for a fixed interaction strength, there may exist a maximum signal amplification and a corresponding optimum overlap of PPS to achieve it. For weak measurements in the orthogonal regime, we find interesting quantities that play the same role that weak values play in the nonorthogonal regime.

arXiv:1010.1155•Physical Review A•May 5, 2011•107 citations

Amplification limit of weak measurements: A variational approach

Shengshi Pang, Todd A. Brun, Shengjun Wu +1 more

Postselected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the limit of this ability, which is fundamental to understanding and applying weak measurements. The limitation of the conventional weak-value formalism for this problem is the divergence of weak values when the pre- and postselections are nearly orthogonal. In this paper, we study this problem by a variational approach for a general Hamiltonian ${H}_{\mathrm{int}}=gA\ensuremath{\bigotimes}\ensuremath{\Omega}\ensuremath{\delta}(t\ensuremath{-}{t}_{0}),\phantom{\rule{0.16em}{0ex}}g\ensuremath{\ll}1$. We derive a general asymptotic solution and show that the amplification limit is essentially independent of $g$ and is determined by only the initial state of the detector and the number of distinct eigenvalues of $A$ or $\ensuremath{\Omega}$. An example of spin-$\frac{1}{2}$ particles with a pair of Stern-Gerlach devices is given to illustrate the results. The limiting case of continuous-variable systems is also investigated to demonstrate the influence of system dimension on the amplification limit.

arXiv:1307.2630•Physical Review A•Jul 14, 2014•13 citations

A perspective on measurement with preselection and postselection: from weak measurements to strong measurements

Xuanmin Zhu, Yu-Xiang Zhang, Shengshi Pang +3 more

We study quantum measurements with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength. For a qubit system, we derive the maximum measurement results by choosing appropriate initial and finial states. Significant amplification effect is obtained when the interaction between the system and the measuring device is very weak; and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measure sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can both be significantly improved by weak measurements; surprisingly, neither SNR nor MS can be effectively improved when the probability decrease is considered.

•Aug 8, 2011•8 citations

Weak value beyond conditional expectation value of the pointer readings

Lev Vaidman A, Alon Ben-Israel, Jan Dziewior +6 more

It is argued that a weak value of an observable is a robust property of a single pre- and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affected other systems as if it had been in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system preselected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre- and postselected in mixed states are considered.

arXiv:1611.03989•Physical Review A•Sep 19, 2017•83 citations

Quantum measurements with preselection and postselection

Xuanmin Zhu, Yu-Xiang Zhang, Shengshi Pang +3 more

We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.

arXiv:1108.1608•Physical Review A•Nov 16, 2011•107 citations

Time-dependent quantum weak values: Decay law for postselected states

P. C. W. Davies

Weak measurements offer insights into the behavior of quantum systems. Combined with postselection, quantum mechanics predicts a range of experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent preselected and postselected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of postselection and the choice of final state. The generalized law is illustrated for two interesting choices of postselection.

arXiv:0807.1357•Physical Review A•Mar 5, 2009•20 citations
Weak measurement is a novel quantum measurement scheme, which is usually characterized by the weak value formalism. To guarantee the validity of the weak value formalism, the fidelity between the preselection and the postselection should not be too small generally. In this work, we study the weak measurement on a qubit system with exactly or asymptotically orthogonal pre- and postselections. We shall establish a general rigorous framework for the weak measurement beyond the weak value formalism, and obtain the average output of a weak measurement when the pre- and postselections are exactly orthogonal. We shall also study the asymptotic behavior of a weak measurement in the limiting process that the pre- and postselections tend to be orthogonal.
We extend the idea of weak measurements to the general case, provide a complete treatment, and obtain results for both the regime when the preselected and postselected states (PPS) are almost orthogonal and the regime when they are exactly orthogonal. We surprisingly find that for a fixed interaction strength, there may exist a maximum signal amplification and a corresponding optimum overlap of PPS to achieve it. For weak measurements in the orthogonal regime, we find interesting quantities that play the same role that weak values play in the nonorthogonal regime.
Postselected weak measurement has been widely used in experiments to observe weak effects in various physical systems. However, it is still unclear how large the amplification ability of a weak measurement can be and what determines the limit of this ability, which is fundamental to understanding and applying weak measurements. The limitation of the conventional weak-value formalism for this problem is the divergence of weak values when the pre- and postselections are nearly orthogonal. In this paper, we study this problem by a variational approach for a general Hamiltonian ${H}_{\mathrm{int}}=gA\ensuremath{\bigotimes}\ensuremath{\Omega}\ensuremath{\delta}(t\ensuremath{-}{t}_{0}),\phantom{\rule{0.16em}{0ex}}g\ensuremath{\ll}1$. We derive a general asymptotic solution and show that the amplification limit is essentially independent of ggg and is determined by only the initial state of the detector and the number of distinct eigenvalues of AAA or $\ensuremath{\Omega}$. An example of spin-12\frac{1}{2}21​ particles with a pair of Stern-Gerlach devices is given to illustrate the results. The limiting case of continuous-variable systems is also investigated to demonstrate the influence of system dimension on the amplification limit.
We study quantum measurements with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength. For a qubit system, we derive the maximum measurement results by choosing appropriate initial and finial states. Significant amplification effect is obtained when the interaction between the system and the measuring device is very weak; and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measure sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can both be significantly improved by weak measurements; surprisingly, neither SNR nor MS can be effectively improved when the probability decrease is considered.
It is argued that a weak value of an observable is a robust property of a single pre- and postselected quantum system rather than a statistical property. During an infinitesimal time a system with a given weak value affected other systems as if it had been in an eigenstate with eigenvalue equal to the weak value. This differs significantly from the action of a system preselected only and possessing a numerically equal expectation value. The weak value has a physical meaning beyond a conditional average of a pointer in the weak measurement procedure. The difference between the weak value and the expectation value has been demonstrated on the example of photon polarization. In addition, the weak values for systems pre- and postselected in mixed states are considered.
We study quantum measurement with preselection and postselection, and derive the precise expressions of the measurement results without any restriction on the coupling strength between the system and the measuring device. For a qubit system, we derive the maximum pointer shifts by choosing appropriate initial and finial states. A significant amplification effect is obtained when the interaction between the system and the measuring device is very weak, and typical ideal quantum measurement results are obtained when the interaction is strong. The improvement of the signal-to-noise ratio (SNR) and the enhancement of the measurement sensitivity (MS) by weak measurements are studied. Without considering the probability decrease due to postselection, the SNR and the MS can be both significantly improved by weak measurements; however, neither SNR nor MS can be effectively improved when the probability decrease is considered.
Weak measurements offer insights into the behavior of quantum systems. Combined with postselection, quantum mechanics predicts a range of experimentally testable phenomena. In this paper I consider weak measurements performed on time-dependent preselected and postselected ensembles, with emphasis on the decay of excited states. The results show that the standard exponential decay law is a limiting case of a more general law that depends on both the time of postselection and the choice of final state. The generalized law is illustrated for two interesting choices of postselection.