Statistical hypothesis testing by weak-value amplification: Proposal and evaluation

TL;DR

This paper evaluates the effectiveness of weak-value amplification in statistical hypothesis testing, demonstrating its advantages in detection power and data efficiency compared to traditional parameter estimation methods.

Contribution

It proposes a new hypothesis testing method utilizing weak-value amplification, overcoming data size limitations and enhancing physical understanding and mathematical validation.

Findings

Weak-value amplification increases detection power.

The method works effectively with small data sets.

It provides a better understanding of weak values' significance.

Abstract

We study the detection capability of the weak-value amplification on the basis of the statistical hypothesis testing. We propose a reasonable testing method in the physical and statistical senses to find that the weak measurement with the large weak value has the advantage to increase the detection power and to reduce the possibility of missing the presence of interaction. We enhance the physical understanding of the weak value and mathematically establish the significance of the weak-value amplification. Our present work overcomes the critical dilemma of the weak-value amplification that the larger the amplification is, the smaller the number of data becomes, because the statistical hypothesis testing works even for a small number of data. This is contrasted with the parameter estimation by the weak-value amplification in the literature which requires a large number of data.