# Interplay between strong and weak measurement: Comparison of three experimental approaches to weak value estimation

## TL;DR

This paper compares three experimental methods for estimating weak values, demonstrating their theoretical equivalence and showing that strong interaction approaches can be more practical than traditional weak interactions in linear optics experiments.

## Contribution

It provides a direct comparison and analytical proof of equivalence between weak and strong interaction-based weak value estimation methods, supported by experimental validation.

## Key findings

- Strong interaction methods are experimentally less demanding.
- All three approaches are theoretically equivalent.
- Experimental results confirm the practical advantages of strong interaction methods.

## Abstract

Weak values are traditionally obtained using a weak interaction between the measured system and a pointer state. It has, however, been pointed out that weak coupling can be replaced by a carefully tailored strong interaction. This paper provides a direct comparison of two strong interaction-based approaches (strong interaction accompanied by either a suitably prepared pointer state or quantum erasure) and the traditional weak interaction-based method. Presented theoretical derivations explicitly prove analytical equivalence of these approaches which was subsequently certified by an experiment implemented on the platform of linear optics. We find that strong-interaction-based measurements are experimentally less demanding on this platform.