Re-interpretations of an experiment on the back-action in a weak measurement

TL;DR

This paper re-examines an experiment on back-action in weak measurements, introducing extended weak values and analyzing measurement fluctuations to provide new interpretations and insights into optimal measurement conditions.

Contribution

It introduces the concept of extended weak values involving both system and device states, offering new interpretations and analyzing fluctuations to identify optimal measurement strength.

Findings

Two equivalent interpretations of the experiment are presented.

An optimal measurement strength minimizes fluctuations in results.

The analysis aligns with experimental observations.

Abstract

Interpretations of an experiment on the back-action in a weak measurement in [M. Iinuma et al., New J. Phys. vol.13 (2011), 033041] are revisited. We show two different but essentially equivalent interpretations for this experiment along the original scenario of weak measurements proposed by Aharonov, Albert, and Vaidman. To do this, we introduce the notion of extended weak values which is associated not only with the states of the system but also the state of the measuring device. We also evaluate fluctuations in this experiment and found that an optimal measurement strength exists for a fixed polarization angle prepared as an initial state, at which fluctuations in measurement results vanish. The consistency of this evaluation with the experimental results is discussed.