Anomalous weak values and contextuality: robustness, tightness, and imaginary parts

Ravi Kunjwal (Perimeter Institute), Matthew Pusey (University of Oxford), Matteo Lostaglio (ICFO)

Weak values are quantities accessed through quantum experiments involving weak measurements followed by post-selection. It has been shown that weak values whose real part is `anomalous’, i.e., lies outside the eigenvalue range of the corresponding operator, defy classical explanation in the sense of requiring contextuality [M. F. Pusey, Phys. Rev. Lett. 113, 200401, arXiv:1409.1535]. Here we elaborate on and extend that result in several directions. Firstly, the original theorem requires the observation of certain perfect correlations that can never be realised in any actual experiment. Hence, we provide new theorems suitable to experimental verication. Secondly, the original theorem connects the anomaly to contextuality only in the presence of a whole set of extra operational constraints. Here we clarify the debate surrounding anomalous weak values by showing that all these extra conditions are indeed necessary — if any one of them is dropped, the anomaly can be reproduced classically. Thirdly, whereas the original result required the real part of the weak value to be anomalous, we also give a version for any weak value with nonzero imaginary part. Finally, we show that similar results hold if the weak measurements is performed through qubit pointers, rather than the traditional continuous system. In summary, we provide tight inequalities for witnessing nonclassicality using experimentally realistic measurements of any anomalous weak value, and clarify what ingredients of the quantum experiment must be missing in any classical model that can reproduce the anomaly.

This submission is based on arXiv:1812.06940.