Experimentally quantifying the advantages of weak-value-based metrology

Abstract

We experimentally investigate the relative advantages of implementing weak-value-based metrology versus standard methods. While the techniques outlined herein apply more generally, we measure small optical beam deflections both using a Sagnac interferometer with a monitored dark port (the weak-value-based technique), and by focusing the entire beam to a split detector (the standard technique). By introducing controlled external transverse detector modulations and transverse beam deflection momentum modulations, we quantify the mitigation of these sources in the weak-value-based experiment versus the standard focusing experiment. The experiments are compared using a combination of deterministic and stochastic methods. In all cases, the weak-values technique performs the same or better than the standard technique by up to two orders of magnitude in precision for our parameters. We further measure the statistical efficiency of the weak-values-based technique. By postselecting on $1\%$ of the photons, we obtain $99\%$ of the available Fisher information of the beam deflection parameter

Seeing opportunity in every difficulty: protecting information with weak value techniques

“…The third inequality follows from the selection of the optimal initial state |i * by the standard measurement strategy. It is possible to get close to saturating these inequalities whilst maintaining a large weak value [22,23]. This means that almost all of the Fisher information may be concentrated into an unlikely or 'dark' detector mode.…”

“…From 2013 onwards, however, theoretical treatments of the weak value technique called into doubt whether there was any true advantage over standard strategies [17][18][19][20], especially from the point of view of parameter estimation. There were also a slew of theoretical [21,22] and experimental [23] papers arguing for the merits of weak value techniques. A review of these results is given in Ref.…”

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.…”

Exploring quantum foundations with single photons

“…Simply put, the goal of a weak value experiment is to concentrate most of the information into a small fraction of the events, which are more easily detected, and ignore the rest. Although a large part of the relevant information can be retained in this way [130], the weak value method can only match the performance of a postselection-free method in the limit of an infinitely weak measurement [129]. On the other hand, if the relevant resource is the measured particles rather than the input particles (such as in optical schemes, since photons are cheap), then the postselection probability is irrelevant and the concentration of information implies that the weak-value method performs better [131].…”

“…On the more technical side, weak value amplification typically performs worse even in the presence of noise [129]. However, there are also some noise models (such as 1 f noise) where it is beneficial [130,133]. Finally, it might be the case that the optimal estimators (for the non-postselected experiment) cannot be implemented or that the initial state cannot be chosen optimally, in which case the optimal post-selection can still help.…”