Violation of Bell-type inequality in single-neutron interferometry: quantum contextuality

We report a single-neutron optical experiment to demonstrate the violation of a Bell-like inequality. Entanglement is achieved between the degrees of freedom for a single particle. The total wave function of the neutron is described in a tensor product Hilbert space. A Bell-like inequality is derived not by a non-locality but by a contextuality. Joint measurements of the spinor and the path properties lead to the violation of a Bell-like inequality. Manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space.