# Confined Contextuality in Neutron Interferometry: Observing the Quantum Pigeonhole Effect. (arXiv:1609.06046v5 [quant-ph] UPDATED)

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 shortcoming 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 $5\sigma$ average violation of the noncontextual

bound, with one contributing term violating an independent bound by more than

$99\sigma$. This weakly measured confined BKS contextuality also confirms the

quantum pigeonhole effect, wherein eigenvalue assignments to contextual

observables apparently violate the classical pigeonhole principle.