When amplification with weak values fails to suppress technical noise

TL;DR

This paper critically examines the effectiveness of weak-value amplification in quantum measurements, demonstrating that it does not provide fundamental advantages in parameter estimation under realistic noise conditions.

Contribution

The study shows that weak-value amplification does not improve measurement precision in the presence of detector imperfections and noise, challenging its practical utility.

Findings

Weak-value amplification offers no fundamental metrological advantage.

Amplification is equally susceptible to detector imperfections as non-amplified methods.

Postselection reduces success probability without improving robustness to noise.

Abstract

The application of postselection to a weak quantum measurement leads to the phenomenon of weak values. Expressed in units of the measurement strength, the displacement of a quantum coherent measuring device is ordinarily bounded by the eigenspectrum of the measured observable. Postselection can enable an interference effect that moves the average displacement far outside this range, bringing practical benefits in certain situations. Employing the Fisher information metric, we argue that the amplified displacement offers no fundamental metrological advantage, due to the necessarily reduced probability of success. Our understanding of metrological advantage is the possibility of a lower uncertainty in the estimate of an unknown parameter with a large number of trials. We analyze a situation in which the detector is pixelated with a finite resolution, and in which the detector is afflicted by random displacements: imperfections which degrade the fundamental limits of parameter estimation. Surprisingly, weak-value amplification is no more robust to them than a technique making no use of the amplification effect brought about by a final, postselected measurement.