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New Journal of Physics

Falsification of Leggett's model using neutron matter waves

Yuji Hasegawa, Claus Schmitzer, Hannes Bartosik, Jürgen Klepp, Stephan Sponar, Katharina Durstberger-Rennhofer, G. Badurek

Published Feb 17, 2012• 12 citations
Publisher

Abstract

According to Bell's theorem, no theory based on the joint assumption of realism and locality can reproduce certain predictions of quantum mechanics. Another class of realistic models, proposed by Leggett, that demands realism but abandons reliance on locality, is predicted to be in conflict with quantum mechanics. In this paper, we report on an experimental test of a contextual realistic model analogous to the model of Leggett performed with matter waves, more precisely with neutrons. Correlation measurements of the spin-energy entangled single-particle system show violation of a Leggett-type inequality by more than 7.6 standard deviations. Our experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.

DOI
10.1088/1367-2630/14/2/023039

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According to Bell's theorem, no theory based on the joint assumption of realism and locality can reproduce certain predictions of quantum mechanics. Another class of realistic models, proposed by Leggett, that demands realism but abandons reliance on locality, is predicted to be in conflict with quantum mechanics. In this paper, we report on an experimental test of a contextual realistic model analogous to the model of Leggett performed with matter waves, more precisely with neutrons. Correlation measurements of the spin-energy entangled single-particle system show violation of a Leggett-type inequality by more than 7.6 standard deviations. Our experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.
According to Bell’s theorem, every theory based on local realism is at variance with certain predictions of quantum mechanics. A theory that maintains realism but abandons reliance on locality, which has been proposed by Leggett, is incompatible with experimentally observable quantum correlations. In our experiment correlation measurements of spin-energy entangled single-neutrons violate a Leggett-type inequality by more than 7.6 standard deviations. The experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.
Bell's theorem states that no local hidden-variable model is compatible with quantum mechanics. Surprisingly, even if we release the locality constraint, certain nonlocal hidden-variable models, such as the one proposed by Leggett, may still be at variance with the predictions of quantum physics. Here, we report an experimental test of Leggett's nonlocal model with solid-state spins in a diamond nitrogen-vacancy center. We entangle an electron spin with a surrounding weakly coupled 13C^{13}\mathrm{C}13C nuclear spin and observe that the entangled states violate Leggett-type inequalities by more than four and seven standard deviations for six and eight measurement settings, respectively. Our experimental results are in full agreement with quantum predictions and violate Leggett's nonlocal hidden-variable inequality with a high level of confidence.
The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement of single neutrons. Here entanglement is achieved not between different particles, but between degrees of freedom of a single neutron, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality derived from the Kochen-Specker theorem. The observed violation 2.291±0.008≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
Experimental investigations of quantum mechanical phenomena with neutron inter-ferometer and polarimeters are presented. Interferometry exhibits clear evidence of quantum-contextuality and polarimetry demonstrates conflicts of a contextual model of quantum mechanics á la Leggett. In these experiments, entanglements are achieved between degrees of freedom in a single-particle: spin, path and energy degrees of freedom are manipulated coherently and entangled. Both experiments manifest the fact that quantum contextuality is valid for phenomena with matter waves with high precision. In addition, another experiment is described which deals with error-disturbance uncertainty relation: we have experimentally tested error-disturbance uncertainty relations, one is derived by Heisenberg and the other by Ozawa. Experimental results confirm the fact that the Heisenberg's uncertainty relation is often violated and that the new relation by Ozawa is always larger than the limit.
Recent experiments of Gröblacher et al proved the violation of a Leggett-type inequality that was claimed to be valid for a broad class of non-local hidden-variable theories. The impossibility of constructing a non-local and realistic theory, unless it entails highly counterintuitive features, seems thus to have been experimentally proved. This would bring us close to a definite refutation of realism. Indeed, realism was proved to be also incompatible with locality, according to a series of experiments testing Bell inequalities. The present paper addresses the said experiments of Gröblacher et al and presents an explicit, contextual and realistic, model that reproduces the predictions of quantum mechanics. It thus violates the Leggett-type inequality that was established with the aim of ruling out a supposedly broad class of non-local models. We can thus conclude that plausible contextual, realistic, models are still tenable. This restates the possibility of a future completion of quantum mechanics by a realistic and contextual theory which is not in a class containing only highly counterintuitive models. The class that was ruled out by the experiments of Gröblacher et al is thus proved to be a limited one, arbitrarily separating models that physically belong in the same class.
The long-lasting view of entanglement as the characteristic trait of quantum mechanics has been recently challenged by experimental demonstrations of non-quantum entanglement. This motivates a review of the meaning of Bell violations, which have been widely taken to prove the impossibility of a realistic interpretation of quantum mechanics and as a manifestation of its non-local character. This work provides new theoretical evidence for the need of reviewing the meaning of Bell violations, especially when they occur outside the quantum framework. We present a local-realistic model that reproduces quantum predictions concerning Bell tests. We claim that local-realism is fully compatible with correlations that are not of the Bell type and therefore lie outside the scope of Bell's theorem. Most experimental Bell tests involve either spin vectors spanning the Bloch sphere or Stokes vectors spanning the Poincaré sphere. A suitable statistical tool that allows assessing correlations between vectors is given by inner-product-type correlations. Using them, it is possible to reproduce quantum predictions for all Bell states, thereby explaining experimental results of Bell tests within a local-realistic framework.