Weak value amplification is suboptimal for estimation and detection

TL;DR

This paper rigorously demonstrates that weak value amplification (WVA) is not optimal for parameter estimation or signal detection, and provides the optimal measurement strategy and conditions for noise mitigation.

Contribution

It proves that post-selection in WVA reduces accuracy and identifies the optimal experimental setup, challenging the perceived advantages of WVA.

Findings

Post-selection decreases estimation accuracy.

Optimal arrangement involves equal, minimal weak values.

Weak measurement can mitigate technical noise under specific conditions.

Abstract

We show using statistically rigorous arguments that the technique of weak value amplification (WVA) does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically we prove that post-selection, a necessary ingredient for WVA, decreases estimation accuracy and, moreover, arranging for anomalously large weak values is a suboptimal strategy. In doing so, we explicitly provide the optimal estimator, which in turn allows us to identify the optimal experimental arrangement to be the one in which all outcomes have equal weak values (all as small as possible) and the initial state of the meter is the maximal eigenvalue of the square of the system observable. Finally, we give precise quantitative conditions for when weak measurement (measurements without post-selection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation.