Confined contextuality in neutron interferometry: Observing the quantum pigeonhole effect

Previous experimental tests of quantum contextuality based on the Bell-Kochen-Specker (BKS) theorem have demonstrated that not all observables among a given set can be assigned noncontextual eigenvalue predictions, but have never identified which specific observables must fail such assignment. We now remedy this short- coming by showing that BKS contextuality can be confined to particular observables by pre- and postselection, resulting in anomalous weak values that we measure using modern neutron interferometry.

We construct a confined contextuality witness from weak values, which we measure experimentally to obtain a 5σ average violation of the noncontextual bound, with one contributing term violating an independent bound by more than 99σ. This weakly measured confined BKS contextuality also confirms the quantum pigeonhole effect, wherein eigenvalue assignments to contextual observables apparently violate the classical pigeonhole principle.

The article was published in: Physical Revue A 96(5): 052131.

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This work was supported (in part) by the Fetzer Franklin Fund of the John E. Fetzer Memorial Trust.