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Violation of a Bell-like inequality in single-neutron interferometry


Non-local correlations between spatially separated systems have been extensively discussed in the context of the Einstein, Podolsky and Rosen (EPR) paradox1 and Bell's inequalities2. Many proposals and experiments designed to test hidden variable theories and the violation of Bell's inequalities have been reported3,4,5,6,7; usually, these involve correlated photons, although recently an experiment was performed with 9Be+ ions8. 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 theories9,10,11,12.

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Figure 1: Schematic view of the experimental set-up to observe quantum correlations clarified by the Bell-like inequality in single-neutron interferometry.
Figure 2: Interference oscillations for two-level systems.
Figure 3: Typical interference oscillations with spinor rotation angle α = 0, π/2, π and 3π/2.

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We appreciate discussions with R. A. Bertlmann, I. J. Cirac and D. Home. This work has been supported by the Austrian Fonds zur Föderung der Wissenschaftlichen Forschung.

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Correspondence to Yuji Hasegawa.

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Hasegawa, Y., Loidl, R., Badurek, G. et al. Violation of a Bell-like inequality in single-neutron interferometry. Nature 425, 45–48 (2003).

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