Non-local correlations between spatially separated systems have been extensively discussed in the context of the Einstein, Podolsky and Rosen (EPR) paradox and Bell's inequalities. Many proposals and experiments designed to test hidden variable theories and the violation of Bell's inequalities have been reported; usually, these involve correlated photons, although recently an experiment was performed with (9)Be(+) ions. Nevertheless, it is of considerable interest to show that such correlations (arising from quantum mechanical entanglement) are not simply a peculiarity of photons. Here we measure correlations between two degrees of freedom (comprising spatial and spin components) of single neutrons; this removes the need for a source of entangled neutron pairs, which would present a considerable technical challenge. A Bell-like inequality is introduced to clarify the correlations that can arise between observables of otherwise independent degrees of freedom. We demonstrate the violation of this Bell-like inequality: our measured value is 2.051 +/- 0.019, clearly above the value of 2 predicted by classical hidden variable theories.

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An experimental demonstration of quantum contextuality with neutrons is presented, which intended to exhibit a Kochen-Specker-like phenomenon. Since no perfect correlation is expected in practical experiments, inequalities are derived to distinguish quantitatively the obtained results from predictions by a noncontextual hidden variable theory. Experiments were accomplished with the use of a neutron interferometer combined with spinor manipulation devices. The results clearly violate the prediction of noncontextual theories.