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

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. The presented theoretical derivations explicitly prove analytical equivalence of these approaches, which were 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.