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

Abstract

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.

Non-contextuality, finite precision measurement and the Kochen–Specker theorem

“…It is thus quite hard to pin down what exactly a purported experimental test of contextuality proves, or could prove, that we do not know already. In our opinion, this key point is not adequately addressed in the papers under discussion (Cabello & García-Alcaine, 1998;Simon et al, 2000;Basu et al, 2001;Huang et al, 2003;Hasegawa et al, 2003).…”

“…We examine in particular an experiment that has actually been performed, Huang et al (2003), inspired by a proposal of Simon et al (2000), in turn based on a scheme of Cabello & García-Alcaine (1998). (Another recent experiment is that of Hasegawa et al (2003), which is similar to a proposal of Basu et al (2001) -we do not discuss this in detail, since the same arguments apply). In Sec.…”

“…But this is crucial if we are to conclude unequivocally that contextuality is being exhibited. Similar comments apply to Hasegawa et al's experiment (Hasegawa et al, 2003): their spin rotator and phase shifter need to be adjusted to alter their parameters α and χ, and they naturally need to rely on the standard quantum formalism in order to interpret the experiment as carrying out measurements of particular projections onto the path and spin degrees of freedom.…”

“…Quite a few experiments purporting to test contextuality have recently been proposed (Cabello & García-Alcaine, 1998;Simon et al, 2000;Basu et al, 2001) and performed (Huang et al, 2003;Hasegawa et al, 2003). Several authors have suggested an analogy between these purported experimental tests of contextuality and Bell experiments testing local causality.…”

“…The CK models then show us that even if it is assumed that the operation of each experimental device is well described by the Hilbert space formalism, a non-contextual, classical simulation of the experiment is possible. 10 We make a brief remark about the experiment of Hasegawa et al (2003), and the proposal of Basu et al (2001). In both cases, an inequality is derived, formally identical to the Clauser-Horne-Shimony-Holt inequality (Clauser et al, 1969), that concerns the spin and path degrees of freedom of a single neutron.…”