Entanglement between degrees of freedom of single neutrons

Non-local correlations between subsystems sufficiently separated in spacetime have been extensively discussed in the light of the Einstein, Podolsky and Rosen (EPR) paradox, together with Bellʹs inequality. Within quantum terminology, such a non-locality can be interpreted as a consequence of the entanglement of subsystems. A more general concept, i.e., quantum contextuality, compared to non-locality, can be introduced to describe other striking phenomena predicted by quantum theory. As examples of quantum contextuality, we report several neutron interferometer experiments: a violation of a Bell-like inequality, a Kochen–Specker-like phenomenon, a quantum state tomography. Entanglement is achieved not between the particles, but between the degrees of freedom of a single-particle. Furthermore, an experiment dealing with triple entanglement is presented.