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

Chinese Physics B

Impact of decoherence on the metrological advantage of weak-value amplification

Yu-Han 雨涵 Yan 严, Yan-Ping 艳萍 Tan 谭, Yan-Yan Lu, Shao-Jie Xiong, Zhe Sun

Published Dec 9, 2025• 0 citations
Publisher

Abstract

Abstract We present a theoretical investigation of weak-value amplification (WVA) under decoherence, quantifying its metrological capabilities through the quantum Fisher information (QFI). By modeling decoherence via Kraus operators acting before and after the weak measurement interaction, we derive exact expressions for the QFI governing parameter estimation of a weak coupling strength. These analytical results reveal the fundamental limitation imposed by decoherence on the QFI achievable via WVA. From these results, the optimal post-selection state that maximizes the QFI can be derived for different noise environments. Through paradigmatic examples, including amplitude damping and depolarizing channels, we demonstrate a key distinction: the optimal post-selection evolves with the noise strength in the amplitude damping channel, but is fixed in the depolarizing channel. This work provides both theoretical insights and practical guidance for optimizing metrological schemes based on WVA in realistic decoherent environments.

DOI
10.1088/1674-1056/ae29fe

Related papers

Advantage of quantum coherence in postselected metrology

Shao-Jie Xiong, Wei, Peng-Fei, Huang-Qiu-Chen Wang +5 more

In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum coherence of the initial system is closely related to the preparation costs and measurement costs in parameter estimation. With the increase of initial quantum coherence, the joint values of preparation costs and measurement costs can be optimized to smaller. Moreover, we derive an analytical tradeoff relation between the preparation, measurement and the quantum coherence. We further experimentally test the tradeoff relation in a linear optical setup. The experimental and theoretical results are in good agreement and show that the quantum coherence plays a key role in bounding the resource costs in the postselected metrology process.

arXiv:2212.05285•Dec 10, 2022•0 citations

Interference-based weak-value amplification effects in post-selected weak measurement

Yurong Liu, Zhaoxue Li, Yucheng Ye +2 more

Abstract Weak measurement (WM) based on post-selection is a useful tool for precision metrology due to the ability of amplifying weak physical effects. In this paper, we reveal the underlying mechanism of the amplification in the post-selected WM based on the weak-value amplification (WVA) and the almost balanced weak-values amplification (ABWVA) strategies. We find that the amplification stems from the interference between the local oscillator and signal components which are respectively associated with the initial system state and the state disturbance induced by the weak coupling. The magnitude of the amplification is proportional to the interference strength which is dominated by the post-selection and the coupling strength. Furthermore, our theory can perfectly explain the amplification limit in the WVA strategy and the anomalous amplification in the ABWVA strategy.

Laser Physics•Jul 29, 2021•1 citation

Quantum-coherence-free precision metrology by means of difference-signal amplification

Jialin Li, Yazhi Niu, Xinyi Wang +2 more

The novel weak-value-amplification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states. And, an alternative version, termed as joint WVA (JWVA), which employs the difference-signal from the post-selection accepted and rejected results, has been found possible to achieve even better sensitivity (two orders of magnitude higher) under some technical limitations (e.g. misalignment errors). In this work, after erasing the quantum coherence, we analyze the difference-signal amplification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplification effect can be achieved. We obtain a simple expression for the amplified signal, carry out characterization of precision, and point out the optimal working regime. We also discuss how to implement the post-selection of a classical mixed state. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice.

arXiv:2212.13729•Scientific Reports•Mar 22, 2023•0 citations

Weak Value Amplification Can Outperform Conventional Measurement in the Presence of Detector Saturation

Jérémie Harris, Robert W. Boyd, Jeff S. Lundeen

Weak value amplification (WVA) is a technique by which one can magnify the apparent strength of a measurement signal. Some have claimed that WVA can outperform more conventional measurement schemes in parameter estimation. Nonetheless, a significant body of theoretical work has challenged this perspective, suggesting WVA to be fundamentally suboptimal. Optimal measurements may not be practical, however. Two practical considerations that have been conjectured to afford a benefit to WVA over conventional measurement are certain types of noise and detector saturation. Here, we report a theoretical study of the role of saturation and pixel noise in WVA-based measurement, in which we carry out a Bayesian analysis of the Fisher information available using a saturable, pixelated, digitized, and/or noisy detector. We draw two conclusions: first, that saturation alone does not confer an advantage to the WVA approach over conventional measurement, and second, that WVA can outperform conventional measurement when saturation is combined with intrinsic pixel noise and/or digitization.

arXiv:1612.04327•Physical Review Letters•Feb 15, 2017•128 citations

Fisher information analysis on post-selection involved quantum precision measurements 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 post-selection. %% In this work we show that, rather than the Gaussian meter state as typically considered, using the optical coherent state as a meter, the WVA measurement can definitely outperform the conventional measurement not involving the strategy of post-selection. %% We also show that the post-selection 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 sharp contrast to the claim proved in the absence of post-selection. The post-selection strategy can also result in the precision of Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but without using any expensive quantum resources. %% The present work may stimulate further investigations for the potential of the post-selection strategy in quantum precision measurements.

arXiv:2201.13016•Jan 31, 2022•0 citations

Heisenberg-Limited Metrology via Weak-Value Amplification without Using Entangled Resources

Yosep Kim, Seung-Yeun Yoo, Yoon-Ho Kim

Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here, we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling without resorting to entanglement. This indicates that the perceived advantages of the entanglement-assisted WVA are in fact due to iterative interactions between each particle of an entangled system and a meter, rather than coming from the entanglement itself. Our work opens a practical pathway for achieving the Heisenberg-limited WVA without using fragile and experimentally demanding entangled resources.

arXiv:2109.03762•Physical Review Letters•Jan 25, 2022•38 citations
Abstract We present a theoretical investigation of weak-value amplification (WVA) under decoherence, quantifying its metrological capabilities through the quantum Fisher information (QFI). By modeling decoherence via Kraus operators acting before and after the weak measurement interaction, we derive exact expressions for the QFI governing parameter estimation of a weak coupling strength. These analytical results reveal the fundamental limitation imposed by decoherence on the QFI achievable via WVA. From these results, the optimal post-selection state that maximizes the QFI can be derived for different noise environments. Through paradigmatic examples, including amplitude damping and depolarizing channels, we demonstrate a key distinction: the optimal post-selection evolves with the noise strength in the amplitude damping channel, but is fixed in the depolarizing channel. This work provides both theoretical insights and practical guidance for optimizing metrological schemes based on WVA in realistic decoherent environments.
In conventional measurement, to reach the greatest accuracy of parameter estimation, all samples must be measured since each independent sample contains the same quantum Fisher information. In postselected metrology, postselection can concentrate the quantum Fisher information of the initial samples into a tiny post-selected sub-ensemble. It has been proven that this quantum advantage can not be realized in any classically commuting theory. In this work, we present that the advantage of postselection in weak value amplification (WVA) can not be achieved without quantum coherence. The quantum coherence of the initial system is closely related to the preparation costs and measurement costs in parameter estimation. With the increase of initial quantum coherence, the joint values of preparation costs and measurement costs can be optimized to smaller. Moreover, we derive an analytical tradeoff relation between the preparation, measurement and the quantum coherence. We further experimentally test the tradeoff relation in a linear optical setup. The experimental and theoretical results are in good agreement and show that the quantum coherence plays a key role in bounding the resource costs in the postselected metrology process.
Abstract Weak measurement (WM) based on post-selection is a useful tool for precision metrology due to the ability of amplifying weak physical effects. In this paper, we reveal the underlying mechanism of the amplification in the post-selected WM based on the weak-value amplification (WVA) and the almost balanced weak-values amplification (ABWVA) strategies. We find that the amplification stems from the interference between the local oscillator and signal components which are respectively associated with the initial system state and the state disturbance induced by the weak coupling. The magnitude of the amplification is proportional to the interference strength which is dominated by the post-selection and the coupling strength. Furthermore, our theory can perfectly explain the amplification limit in the WVA strategy and the anomalous amplification in the ABWVA strategy.
The novel weak-value-amplification (WVA) scheme of precision metrology is deeply rooted in the quantum nature of destructive interference between the pre- and post-selection states. And, an alternative version, termed as joint WVA (JWVA), which employs the difference-signal from the post-selection accepted and rejected results, has been found possible to achieve even better sensitivity (two orders of magnitude higher) under some technical limitations (e.g. misalignment errors). In this work, after erasing the quantum coherence, we analyze the difference-signal amplification (DSA) technique, which serves as a classical counterpart of the JWVA, and show that similar amplification effect can be achieved. We obtain a simple expression for the amplified signal, carry out characterization of precision, and point out the optimal working regime. We also discuss how to implement the post-selection of a classical mixed state. The proposed classical DSA technique holds similar technical advantages of the JWVA and may find interesting applications in practice.
Weak value amplification (WVA) is a technique by which one can magnify the apparent strength of a measurement signal. Some have claimed that WVA can outperform more conventional measurement schemes in parameter estimation. Nonetheless, a significant body of theoretical work has challenged this perspective, suggesting WVA to be fundamentally suboptimal. Optimal measurements may not be practical, however. Two practical considerations that have been conjectured to afford a benefit to WVA over conventional measurement are certain types of noise and detector saturation. Here, we report a theoretical study of the role of saturation and pixel noise in WVA-based measurement, in which we carry out a Bayesian analysis of the Fisher information available using a saturable, pixelated, digitized, and/or noisy detector. We draw two conclusions: first, that saturation alone does not confer an advantage to the WVA approach over conventional measurement, and second, that WVA can outperform conventional measurement when saturation is combined with intrinsic pixel noise and/or digitization.
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 post-selection. %% In this work we show that, rather than the Gaussian meter state as typically considered, using the optical coherent state as a meter, the WVA measurement can definitely outperform the conventional measurement not involving the strategy of post-selection. %% We also show that the post-selection 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 sharp contrast to the claim proved in the absence of post-selection. The post-selection strategy can also result in the precision of Heisenberg (or even "super-Heisenberg") scaling with the photon numbers, but without using any expensive quantum resources. %% The present work may stimulate further investigations for the potential of the post-selection strategy in quantum precision measurements.
Weak-value amplification (WVA) provides a way for amplified detection of a tiny physical signal at the expense of a lower detection probability. Despite this trade-off, due to its robustness against certain types of noise, WVA has advantages over conventional measurements in precision metrology. Moreover, it has been shown that WVA-based metrology can reach the Heisenberg limit using entangled resources, but preparing macroscopic entangled resources remains challenging. Here, we demonstrate a novel WVA scheme based on iterative interactions, achieving the Heisenberg-limited precision scaling without resorting to entanglement. This indicates that the perceived advantages of the entanglement-assisted WVA are in fact due to iterative interactions between each particle of an entangled system and a meter, rather than coming from the entanglement itself. Our work opens a practical pathway for achieving the Heisenberg-limited WVA without using fragile and experimentally demanding entangled resources.