# On the Validity of Weak Measurement Applied for Precision Measurement

## TL;DR

This paper develops a comprehensive framework to assess the validity of weak measurements in precision experiments, ensuring their amplification effects are reliable and within theoretical bounds.

## Contribution

The authors introduce a systematic framework to evaluate the validity of weak measurements, addressing uncertainties and confirming the reliability of key experimental results.

## Key findings

- Experiments by Hosten and Dixon are within valid amplification ranges.
- The framework confirms the soundness of previous weak measurement experiments.
- It provides a practical tool for future weak measurement design and analysis.

## Abstract

We present a general framework of examining the validity of weak measurement -- the standard procedure to acquire Aharonov's weak value -- which has been used intensively in recent years for precision measurement, taking advantage of the amplification mechanism available for the weak value. Our framework allows one to deal systematically with various causes of uncertainties intrinsic to the actual measurement process as well as those found in the theoretical analysis employed to describe the system. Using our framework, we examine in detail the two seminal experiments, Hosten's detection measurement of the spin Hall effect of light and Dixon's ultra sensitive beam deflection measurement. Our analysis shows that their results are well within the range of amplification (actually in the vicinity of the optimal point) where the weak measurements are valid. This suggests that our framework is both practical and sound, and may be useful to determine beforehand the possible extent of amplification in the future weak measurement experiments.