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arXiv:1402.1352

A comment on "Weak value amplification is suboptimal for estimation and detection"

Yaron Kedem

Published Feb 6, 2014• 3 citations
arXivHTMLPDF

Abstract

By assuming that the weak value is real, Ferrie and Combes render their result inapplicable to weak measurement experiments which are aimed at enhancing precision.
DOI
10.48550/arxiv.1402.1352

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Comment on "Weak value amplification is suboptimal for estimation and detection"

Lev Vaidman A

The assumptions of Ferrie and Combes are irrelevant for realistic experimental situations. This undermines their conclusions.

arXiv:1402.0199•Feb 2, 2014•9 citations

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Kedem's Comment [arXiv:1402.1352] on our Letter [PRL 112, 040406 (2014)] contains only the criticism that we did not consider complex weak values. We point out follow-up work which uses the same analysis as in our Letter, includes any type of weak values and draws the same conclusion. Vaidman's Comment [arXiv:1402.0199] on our Letter can be deconstructed in to two distinct logical fallacies.

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We show by using statistically rigorous arguments that the technique of weak value amplification does not perform better than standard statistical techniques for the tasks of single parameter estimation and signal detection. Specifically, we prove that postselection, a necessary ingredient for weak value amplification, 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 postselection or anomalously large weak values) can mitigate the effect of uncharacterized technical noise in estimation.