Non-Locality and Contextuality in Neutron Quantum Optics

Helmut Rauch

Yuji Hasegawa, Rudolf Loidl, G. Badurek +2 more

We report a single-neutron optical experiment to demonstrate the violation of a Bell-like inequality. Entanglement is achieved not between particles, but between the degrees of freedom, in this case, for a single-particle. The spin-{\small 1/2} property of neutrons are utilized. 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. A discussion is given on the quantum contextuality and an entanglement-induced correlation in our experiment.

Yuji Hasegawa, Rudolf Loidl, Matthias Baron +2 more

Helmut Rauch

Neutron matter-wave optics provides the basis for new quantum experiments and a step towards applications of quantum phenomena. Most experiments have been performed with a perfect crystal neutron interferometer where widely separated coherent beams can be manipulated individually. Various geometric phases have been measured and their robustness against fluctuation effects has been proven, which may become a useful property for advanced quantum communication. Quantum contextuality for single particle systems shows that quantum correlations are to some extent more demanding than classical ones. In this case entanglement between external and internal degrees of freedom offers new insights into basic laws of quantum physics. Non-contextuality hidden variable theories can be rejected by arguments based on the Kochen-Specker theorem.

Vladimir K. Ignatovich

This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the experimental results should be re-evaluated. The results of the experiments with atomic cascade are shown not to contradict the local realism. The article points out flaws in the experiments with down-converted photons. The experiments with neutron interferometer on measuring the "contextuality" and Bell-like inequalities are analyzed, and it is shown that the experimental results can be explained without such notions. Alternative experiment is proposed to prove the validity of local realism.

Helmut Rauch