Interpreting weak value amplification with a toy realist model

TL;DR

This paper interprets weak values in quantum mechanics through a stochastic optics model, showing they correspond to average intensities of an underlying ontological electromagnetic field in a specific experiment.

Contribution

It introduces a classical stochastic optics model that reproduces weak values as average intensities, offering an ontological perspective on weak measurement results.

Findings

Weak values match the conditional means of electric field intensities in the model.

The stochastic optics model reproduces experimental weak value results.

Breakdown of the model occurs with anomalous weak values outside the experimental regime.

Abstract

Constructing an ontology for quantum theory is challenging, in part due to unavoidable measurement back-action. The Aharonov-Albert-Vaidman weak measurement formalism provides a method to predict measurement results (weak values) in a regime where back-action is negligible. The weak value appears analogous to a classical conditional mean and in fact, has a number of features that further suggest it may be interpreted as being related to some underlying ontological model. However, the ontology appears bizarre since the weak values are complex and unbounded. Here, we study weak values in the context of a recent quantum optical experiment involving two-photon interactions. The results of the experiment are reinterpreted within a 'stochastic optics' model of light. The model is based on standard (Maxwell) electromagnetic theory, supplemented by stochastic fluctuations of the electromagnetic fields. We show that the conditional means of the electric field intensities correspond to the experimentally observed weak values. This is a provocative result, as it suggests that at least within this experiment, the weak value gives us information about the average of an ontological quantity (the intensity). We study the breakdown of the stochastic optics model, which occurs outside the experimentally probed regime, and in particular in the limit where the weak value predicts 'anomalous' results.