The average result of a weak measurement of some observable $A$ can, under postselection of the measured quantum system, exceed the largest eigenvalue of $A$. The nature of weak measurements, as well as the presence of postselection 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 nonclassical 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.

• Received 5 September 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.200401