Anomalous Weak Values Are Proofs of Contextuality

TL;DR

This paper demonstrates that anomalous weak values in quantum measurements serve as definitive proofs of contextuality, clarifying the non-classical nature of such phenomena and their experimental verification.

Contribution

It establishes that anomalous weak values are rigorous proofs of contextuality, providing a clear criterion for non-classical behavior in quantum systems.

Findings

Anomalous weak values indicate quantum contextuality.

Weak measurements can serve as proofs of non-classicality.

Clarifies the features necessary to experimentally demonstrate non-classical effects.

Abstract

The average result of a weak measurement of some observable $A$ can, under post-selection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of post-selection and hence possible contribution of measurement-disturbance, has led to a long-running debate about whether or not this is surprising. Here, it is shown that such "anomalous weak values" are non-classical in a precise sense: a sufficiently weak measurement of one constitutes a proof of contextuality. This clarifies, for example, which features must be present (and in an experiment, verified) to demonstrate an effect with no satisfying classical explanation.