Confined Contextuality in Neutron Interferometry: Observing the Quantum Pigeonhole Effect

TL;DR

This paper demonstrates that quantum contextuality can be confined to specific observables using neutron interferometry, revealing the quantum pigeonhole effect through anomalous weak values and a significant violation of noncontextual bounds.

Contribution

It introduces a method to confine BKS contextuality to particular observables via pre- and postselection, measured through weak values, and confirms the quantum pigeonhole effect.

Findings

Measured a 5σ violation of the noncontextual bound.

Observed a term violating an independent bound by over 99σ.

Confirmed the quantum pigeonhole effect through confined contextuality.

Abstract

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.