Spin-path entanglement in single-neutron interferometer experiments
There are two powerful arguments against the possibility of extending quantum mechanics (QM) into a more fundamental theory yielding a deterministic description of nature. One is the experimental violation of Bell inequalities, which discards local hidden-variable theories as a possible extension to QM. The other is the Kochen-Specker (KS) theorem, which stresses the incompatibility of QM with a larger class of hidden-variable theories, known as noncontextual hidden-variable theories. We performed experiments with neutron interferometer, which exploits spin-path entanglements in single neutrons. A Bell-like state is generated to demonstrate a violation of the Bell-like inequality and phenomena in accordance with KS theorem: both experiments study quantum contextuality and show clear evidence of the incompatibility of noncontextual hidden variable theories with QM. The value S = 2.202{+-}0.007 Neither-Less-Than-Nor-Equal-To 2 is obtained in the new measurement of the Bell-like inequality, which shows a larger violation than the previous measurement. For the study of KS theorem, the obtained violation 2.291{+-}0.008 Neither-Less-Than-Nor-Equal-To 1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.