Anomalous Weak Values Are Proofs of Contextuality

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.

4 pages. v2: Some typos fixed and some discussions expanded

References in corpus (5)

• Experimental joint weak measurement on a photon pair as a probe of Hardy's Paradox
• Complex weak values in quantum measurement
• Negativity and contextuality are equivalent notions of nonclassicality
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• Disturbance in weak measurements and the difference between quantum and classical weak values
• Voices of Silence, Novelties of Noise: Oblivion and Hesitation as Origins of Quantum Mysteries
• Weak values in a classical theory with an epistemic restriction
• Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
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• Optimal Settings For Amplification And Estimation Of Small Effects In Postselected Ensembles
• Is single-particle interference spooky?
• Contextuality, Witness of Quantum Weirdness
• Weak Value and the Wave-Particle Duality