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:1803.09421 · Physical Review A

Adaptive weak-value amplification with adjustable postselection

Fei Li, Jingzheng Huang, Guihua Zeng

Published Sep 15, 2017• 23 citations
arXivHTMLPDF

Abstract

Weak-value amplification (WVA) has recently become an important technique for parameter estimation, owing to its ability to enhance the signal-to-noise ratio by amplifying extremely small signals with proper postselection strategies. In this paper, we propose an adaptive WVA scheme to achieve the highest Fisher information when using an unbalanced pointer. Different from previous schemes, the adaptive WVA scheme is associated with a real-time update on the postselection states with the help of feedback information from the outcomes, and the ``extremely small'' condition set on the parameter of interest is relaxed. By applying this scheme to a time-delay measurement scenario, we show by numerical simulation that the precision achieved in our scheme is several times higher than the standard WVA scheme. Our result might open a path for improving the WVA technique in a more flexible and robust way.

DOI
10.1103/physreva.96.032112

Related papers

Fisher information analysis on weak-value-amplification metrology using optical coherent states

Yingxin Liu, Lupei Qin, Xin-Qi Li

The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful postselection. In this work we show that, rather than the transverse-spatial-wave-function meter typically considered, using the optical coherent state as a meter, the WVA measurement can outperform the conventional measurement not involving the strategy of postselection. We also show that the postselection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in contrast to the main result proved in the absence of postselection. The postselection strategy can also result in the precision of Heisenberg scaling with the photon numbers without using expensive quantum resources. The present work may stimulate further interest in postselection strategy for quantum precision measurements.

Physical Review A•Aug 30, 2022•20 citations

Autocorrelative weak-value amplification and simulating the protocol under strong Gaussian noise

Jing-Hui Huang, Xiangyun Hu, Adetunmise C. Dada +4 more

By choosing more orthogonality between preselection and postselection states, one can significantly improve the sensitivity in general optical quantum metrology based on the weak-value amplification (WVA) approach. However, increasing the orthogonality decreases the probability of detecting photons and makes the weak measurement difficult, especially when the weak measurement is disturbed by strong noise and the pointer is drowned in noise with a negative-decibel signal-to-noise ratio (SNR). In this article we introduce and numerically evaluate a modified weak-measurement protocol with a temporal pointer, namely, the autocorrelative weak-value amplification (AWVA) approach. Specifically, a small longitudinal time delay (tiny phase shift) $\ensuremath{\tau}$ of a Gaussian pulse is measured by implementing two simultaneous autocorrelative weak measurements under Gaussian white noise with different SNRs. The small quantities $\ensuremath{\tau}$ are obtained by measuring the autocorrelation coefficient of the pulses instead of fitting the shift of the mean value of the probe in the standard WVA technique. Simulation results show that the AWVA approach outperforms the standard WVA technique in the time domain with smaller statistical errors, remarkably increasing the precision of weak measurement under a strong noise background.

arXiv:2203.15231•Physical Review A•Nov 3, 2022•8 citations

Hamiltonian estimation based on adaptive weak value amplification

Chen Fang, Binke Xia, Jingzheng Huang +4 more

Abstract Hamiltonian estimation is a cardinal task in applications of quantum metrology, quantum computation, quantum simulation, etc. When the evolution time is short in order to suppress noise and enhance sensitivity, the measurement and postprocessing may incur high cost. In this paper, we propose an adaptive weak measurement scheme for Hamiltonian estimation, which adjusts the pre- and post-selection according to the difference of the mean shift between two orthogonal post-selected states. According to the angle of the post-selected state, the proposed scheme can change from weak value amplification (WVA) to joint weak measurement (JWM). A study of the quantum Fisher information shows that the JWM situation is always optimal. Meanwhile, the WVA approach loses a little information but it can inherit the WVA’s technical advantages, which are suitable for short evolution times. The widely applicable scope of the proposed scheme makes us believe that it offers a new path for the understanding of unknown Hamiltonians.

Journal of Physics B Atomic Molecular and Optical Physics•Feb 15, 2021•3 citations

Ultra-small phase estimation via weak measurement with postselection: A comparison of joint weak measurement and weak value amplification

Fang Chen, Jingzheng Huang, Yang Yu +2 more

We derive a general theory for the joint weak measurement with arbitrary postselection and employ it in the time-delay measurement. Especially, we study two special cases, i.e., the balanced and unbalanced postselection regimes, and present an experiment to verify the theoretical results. The experimental results show that under similar conditions, the signal-to-noise ratio of using joint weak measurement scheme remains higher than 12 dB when the measured time-delay is smaller the ultimate precision limit of the weak-value amplification scheme. Moreover, the joint weak measurement scheme is robust to the misalignment errors and the wavelength-dependency of optical components, which indicates its advantage of improving the measurement precision with convenient laboratory equipments.

•Sep 14, 2015•2 citations

Optimization of parameter measurement precision with precoupling-assisted weak-value amplification

Manchao Zhang, Jie Zhang, Chun-Wang Wu +4 more

The weak-value amplification is extensively considered in precision metrology in order to achieve a higher sensitivity. Despite the practical benefits in amplifying small physical quantities, its metrological advantage still arouses a broad debate due to the low postselection probability of success. In this paper, by employing the quantum Fisher information metric, we show that the precision of estimating an unknown parameter can be improved by introducing a precoupling process with properly chosen interaction operators. We point out this result is credible for both real and imaginary weak values. By tracking the meter wave functions, we find this enhancement of estimation precision comes from a precoupling induced modulation of the meter wave function, thus the most sensitive regime with respect to the parameter is reached. In addition, the estimation error is investigated by considering the difference between the theoretical and estimated value. The analysis suggests that this kind of error can be effectively suppressed by averaging the estimations resulted from different initial meter states. These results are finally illustrated by an exact numerical simulation where the advantages of our proposal are displayed by the comparison to the standard weak-value amplification scheme.

Physical Review A•Apr 3, 2023•5 citations

Enhanced weak-value amplification with Schrödinger cat-like states

Krishna Mishra, Gaurav Shukla, Devendra Mishra

Weak-value amplification (WVA) has emerged as an effective technique for detecting extremely small physical parameters by combining weak system–meter interactions with a carefully chosen post-selection strategy. In this paper, we explore how WVA performs when the meter is prepared in a Schrödinger cat-like state (SCS). Using the Fisher information (FI) as the primary figure of merit, we assess the attainable precision in estimating the interaction parameter. We compare the sensitivities of even coherent states (ECSs), odd coherent states (OCSs), and Yurke–Stoler states (YSSs) against coherent states (CS). We demonstrate that ECS and OCS as meters provide higher FI than the CS as a meter in some cases, depending on the measurement strategy. Also, ECS yields the largest conventional FI among the four meter states. Furthermore, we explore the impact of vacuum superposition with the meter on FI. We find that optimizing the vacuum coefficient enhances the FI in some conditions. This study shows that SCSs can be useful as meter states for improving precision in weak-measurement metrology.

Journal of the Optical Society of America B•Oct 8, 2026•0 citations
Weak-value amplification (WVA) has recently become an important technique for parameter estimation, owing to its ability to enhance the signal-to-noise ratio by amplifying extremely small signals with proper postselection strategies. In this paper, we propose an adaptive WVA scheme to achieve the highest Fisher information when using an unbalanced pointer. Different from previous schemes, the adaptive WVA scheme is associated with a real-time update on the postselection states with the help of feedback information from the outcomes, and the ``extremely small'' condition set on the parameter of interest is relaxed. By applying this scheme to a time-delay measurement scenario, we show by numerical simulation that the precision achieved in our scheme is several times higher than the standard WVA scheme. Our result might open a path for improving the WVA technique in a more flexible and robust way.
The weak-value-amplification (WVA) technique has been extensively considered and debated in the field of quantum precision measurement, largely owing to the reduced Fisher information caused by the low probability of successful postselection. In this work we show that, rather than the transverse-spatial-wave-function meter typically considered, using the optical coherent state as a meter, the WVA measurement can outperform the conventional measurement not involving the strategy of postselection. We also show that the postselection procedure involved in the WVA scheme can make a mixture of coherent states work better than a pure coherent state with identical average photon numbers. This is in contrast to the main result proved in the absence of postselection. The postselection strategy can also result in the precision of Heisenberg scaling with the photon numbers without using expensive quantum resources. The present work may stimulate further interest in postselection strategy for quantum precision measurements.
By choosing more orthogonality between preselection and postselection states, one can significantly improve the sensitivity in general optical quantum metrology based on the weak-value amplification (WVA) approach. However, increasing the orthogonality decreases the probability of detecting photons and makes the weak measurement difficult, especially when the weak measurement is disturbed by strong noise and the pointer is drowned in noise with a negative-decibel signal-to-noise ratio (SNR). In this article we introduce and numerically evaluate a modified weak-measurement protocol with a temporal pointer, namely, the autocorrelative weak-value amplification (AWVA) approach. Specifically, a small longitudinal time delay (tiny phase shift) $\ensuremath{\tau}$ of a Gaussian pulse is measured by implementing two simultaneous autocorrelative weak measurements under Gaussian white noise with different SNRs. The small quantities $\ensuremath{\tau}$ are obtained by measuring the autocorrelation coefficient of the pulses instead of fitting the shift of the mean value of the probe in the standard WVA technique. Simulation results show that the AWVA approach outperforms the standard WVA technique in the time domain with smaller statistical errors, remarkably increasing the precision of weak measurement under a strong noise background.
Abstract Hamiltonian estimation is a cardinal task in applications of quantum metrology, quantum computation, quantum simulation, etc. When the evolution time is short in order to suppress noise and enhance sensitivity, the measurement and postprocessing may incur high cost. In this paper, we propose an adaptive weak measurement scheme for Hamiltonian estimation, which adjusts the pre- and post-selection according to the difference of the mean shift between two orthogonal post-selected states. According to the angle of the post-selected state, the proposed scheme can change from weak value amplification (WVA) to joint weak measurement (JWM). A study of the quantum Fisher information shows that the JWM situation is always optimal. Meanwhile, the WVA approach loses a little information but it can inherit the WVA’s technical advantages, which are suitable for short evolution times. The widely applicable scope of the proposed scheme makes us believe that it offers a new path for the understanding of unknown Hamiltonians.
We derive a general theory for the joint weak measurement with arbitrary postselection and employ it in the time-delay measurement. Especially, we study two special cases, i.e., the balanced and unbalanced postselection regimes, and present an experiment to verify the theoretical results. The experimental results show that under similar conditions, the signal-to-noise ratio of using joint weak measurement scheme remains higher than 12 dB when the measured time-delay is smaller the ultimate precision limit of the weak-value amplification scheme. Moreover, the joint weak measurement scheme is robust to the misalignment errors and the wavelength-dependency of optical components, which indicates its advantage of improving the measurement precision with convenient laboratory equipments.
The weak-value amplification is extensively considered in precision metrology in order to achieve a higher sensitivity. Despite the practical benefits in amplifying small physical quantities, its metrological advantage still arouses a broad debate due to the low postselection probability of success. In this paper, by employing the quantum Fisher information metric, we show that the precision of estimating an unknown parameter can be improved by introducing a precoupling process with properly chosen interaction operators. We point out this result is credible for both real and imaginary weak values. By tracking the meter wave functions, we find this enhancement of estimation precision comes from a precoupling induced modulation of the meter wave function, thus the most sensitive regime with respect to the parameter is reached. In addition, the estimation error is investigated by considering the difference between the theoretical and estimated value. The analysis suggests that this kind of error can be effectively suppressed by averaging the estimations resulted from different initial meter states. These results are finally illustrated by an exact numerical simulation where the advantages of our proposal are displayed by the comparison to the standard weak-value amplification scheme.
Weak-value amplification (WVA) has emerged as an effective technique for detecting extremely small physical parameters by combining weak system–meter interactions with a carefully chosen post-selection strategy. In this paper, we explore how WVA performs when the meter is prepared in a Schrödinger cat-like state (SCS). Using the Fisher information (FI) as the primary figure of merit, we assess the attainable precision in estimating the interaction parameter. We compare the sensitivities of even coherent states (ECSs), odd coherent states (OCSs), and Yurke–Stoler states (YSSs) against coherent states (CS). We demonstrate that ECS and OCS as meters provide higher FI than the CS as a meter in some cases, depending on the measurement strategy. Also, ECS yields the largest conventional FI among the four meter states. Furthermore, we explore the impact of vacuum superposition with the meter on FI. We find that optimizing the vacuum coefficient enhances the FI in some conditions. This study shows that SCSs can be useful as meter states for improving precision in weak-measurement metrology.