Physical Review A

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

Manchao Zhang, Jie Zhang, Chun-Wang Wu, Yi Xie, Ting Chen, Wei Wu, Ping‐Xing Chen

Published Apr 3, 2023• 5 citations

Abstract

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.

DOI: 10.1103/physreva.107.042601

Related papers

Extension of Linear Response Regime in Weak-Value Amplification Technique

Manchao Zhang, Jie Zhang, Wenbo Su +5 more

The achievable precision of parameter estimation plays a significant role in evaluating a strategy of metrology. In practice, one may employ approximations in a theoretical model development for simplicity, which, however, will cause systematic error and lead to a loss of precision. We derive the error of maximum likelihood estimation in the weak-value amplification technique where the linear approximation of the coupling parameter is used. We show that this error is positively related to the coupling strength and can be effectively suppressed by improving the Fisher information. Considering the roles played by weak values and initial meter states in the weak-value amplification, we also point out that the estimation error can be decreased by several orders of magnitude by averaging the estimations resulted from different initial meter states or weak values. These results are finally illustrated in a numerical example where an extended linear response regime to the parameter is observed.

Chinese Physics LettersMar 6, 20232 citations

Uncertainty control and precision enhancement of weak measurements in the quadratic regime

Bertúlio de Lima Bernardo, Weliton Soares Martins, Sérgio Azevedo +1 more

Weak-value amplification has been successfully used to amplify the sensitivity of small detector signals, which paved the way towards new developments for precise parameter estimation methods. In general, the scheme is based on the idea that, between pre- and postselection, the measured system and the pointer are coupled in such a way that the interaction depends linearly on the coupling constant, the so-called linear regime. In this article, we propose an improvement to this technique that is based on the quadratic regime of interaction to increase the precision of such measurements. We demonstrate that by employing a purely real (imaginary) weak value in this regime, it is possible to decrease considerably the standard deviation of the final pointer observable in the position (momentum) space, when compared to the traditional linear regime, rendering a precision enhancement. By using an all-optical implementation, we obtained experimental data that confirm our theoretical predictions.

Physical Review AJul 13, 20157 citations

Entanglement-Assisted Weak Value Amplification

Shengshi Pang, Justin Dressel, Todd A. Brun

Large weak values have been used to amplify the sensitivity of a linear response signal for detecting changes in a small parameter, which has also enabled a simple method for precise parameter estimation. However, producing a large weak value requires a low postselection probability for an ancilla degree of freedom, which limits the utility of the technique. We propose an improvement to this method that uses entanglement to increase the efficiency. We show that by entangling and postselecting n ancillas, the postselection probability can be increased by a factor of n while keeping the weak value fixed (compared to n uncorrelated attempts with one ancilla), which is the optimal scaling with n that is expected from quantum metrology. Furthermore, we show the surprising result that the quantum Fisher information about the detected parameter can be almost entirely preserved in the postselected state, which allows the sensitive estimation to approximately saturate the relevant quantum Cramér-Rao bound. To illustrate this protocol we provide simple quantum circuits that can be implemented using current experimental realizations of three entangled qubits.

arXiv:1401.5887Physical Review LettersJul 15, 2014107 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 BOct 8, 20260 citations

On the estimation of interaction parameters in weak measurements

Holger Friedrich Hofmann, Timothy C. Ralph, Ping Koy Lam

Since weak measurements are known to produce measurement values that can be much larger than the maximal eigenvalues of the measured observable, it is an interesting question how this enhancement of the measurement signal relates to the sensitivity of quantum measurements as investigated in the field of quantum metrology. In this presentation, it is pointed out that the estimation of a small interaction parameter using weak measurements actually corresponds to standard quantum metrology, where the logarithmic derivatives of the final measurement probabilities are proportional to the corresponding weak values. The analysis of the general weak measurement formalism then shows that extreme weak values do not improve the sensitivity. Instead, all final measurements with real weak values have the same sensitivity as a final measurement of the eigenvalues. This result supports the view that real weak values can be interpreted as precise, zero uncertainty estimates of a quantum observable, despite their deviation from the eigenvalues of the corresponding operator.

arXiv:1012.0071AIP conference proceedingsJan 1, 20112 citations

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 AAug 30, 202220 citations