Technical Advantages for Weak-Value Amplification: When Less Is More

Abstract

The technical merits of weak-value-amplification techniques are analyzed. We consider models of several different types of technical noise in an optical context and show that weak-value-amplification techniques (which only use a small fraction of the photons) compare favorably with standard techniques (which use all of them). Using the Fisher-information metric, we demonstrate that weak-value techniques can put all of the Fisher information about the detected parameter into a small portion of the events and show how this fact alone gives technical advantages. We go on to consider a time-correlated noise model and find that a Fisher-information analysis indicates that the standard method can have much larger information about the detected parameter than the postselected technique. However, the estimator needed to gather the information is technically difficult to implement, showing that the inefficient (but practical) signal-to-noise estimation of the parameter is usually superior. We also describe other technical advantages unique to imaginary weak-value-amplification techniques, focusing on beam-deflection measurements. In this case, we discuss combined noise types (such as detector transverse jitter, angular beam jitter before the interferometer, and turbulence) for which the interferometric weak-value technique gives higher Fisher information over conventional methods. We go on to calculate the Fisher information of the recently proposed photon-recycling scheme for beam-deflection measurements and show it further boosts the Fisher information by the inverse postselection probability relative to the standard measurement case.

Weak-value amplification: state of play

“…Refs. [13,24] argue that time-correlated noise, for example, renders the optimal estimator impractical due to computational complexity. This is not, by itself, a compelling argument for employing weak values, however: one must show that the entire weak value protocol, including the post processing, is not outperformed by a suitable benchmark strategy.…”

“…Together these articles treat the most prevalent types of noise (including pixelation, detector jitter, and dephasing), and a similar approach can be used to analyse other imperfections. For instance, Jordan et al have claimed that for speci c noise models a weak-value-ampli ed tech-nique gives higher Fisher information than conventional methods [13]. By engineering these noise models articially, these predictions have been explored experimentally [14].…”

Noise suppression in inverse weak value-based phase detection

“…The principal reason weak measurements have improved sensitivity is that they allow certain types of technical noise or other experimental limitations to be overcome, while still achieving the same sensitivity as ideal traditional measurement schemes [4,[24][25][26][27][28][29]. Previous theoretical work demonstrating the effectiveness of weak value amplification in reducing the negative effects of technical noise has been in what we term the weak value regime.…”

Heisenberg scaling with weak measurement: a quantum state discrimination point of view

“…The price one pays for this amplification is the loss of a large fraction of events due to the post-selection. Nevertheless, the relevant information about the parameter in question is concentrated into these small number of events [2]. This technique has been adapted to optical metrology and has been successfully implemented in many experiments to precisely estimate various parameters, such as beam deflection, phase or frequency shifts.…”

“…Further, it has been shown that in comparison to a standard experimental technique, and given the presence of certain types of noise sources or technical limitations obscuring the measurement process, the weak value-type experiment can have better precision (even when using optimal statistical estimators), even though the detector only collects a small fraction of the light in the experiment [2]. There have also been a number of recent advances that propose to improve the intrinsic inefficiency of the post-selection.…”