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arXiv:2407.10087 · Progress in Quantum Electronics

Progress and perspectives on weak-value amplification

Liang Xu, Lijian Zhang

Published Jun 8, 2024• 14 citations
arXivHTMLPDF
DOI
10.1016/j.pquantelec.2024.100518

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In this article we present an experimental proposal for the estimation of an optomechanical parameter in the presence of noise. The estimation is based on the technique of weak-value amplification which can enlarge the radiation pressure effect of a single photon on a mechanical oscillator. In our setup we show that the weak-value amplification technique is preferable for the estimation over a method that relies on a strong measurement with postselection because the first method does not require a good prior knowledge of the parameter we wish to estimate, while both strategies reach the same level of precision from a Fisher information perspective. In the presence of strongly correlated noise, the weak-value amplification method is preferable, from a Fisher information perspective, than a standard measurement strategy that does not employ postselection and that is affected by the same type of noise.
Abstract In this paper we provide a simple, straightforward example of a specific situation in which weak-value amplification (WVA) clearly outperforms conventional measurement in determining the angular orientation of an optical component. We also offer a perspective reconciling the views of some theorists, who claim WVA to be inherently sub-optimal for parameter estimation, with the perspective of the many experimentalists and theorists who have used the procedure to successfully access otherwise elusive phenomena.
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.