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arXiv:1004.2836 · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment

Kochen–Specker theorem studied with neutron interferometer

Yuji Hasegawa, Katharina Durstberger-Rennhofer, Stephan Sponar, Helmut Rauch

Published Jul 2, 2010• 44 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.nima.2010.06.234

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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.
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≰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≰1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
We performed an experimental test of the Kochen-Specker theorem based on an inequality derived from the Peres-Mermin proof, using spin-path (momentum) entanglement in a single neutron system. Following the strategy proposed by Cabello et al. [Phys. Rev. Lett. 100, 130404 (2008)10.1103/PhysRevLett.100.130404], a Bell-like state was generated, and three expectation values were determined. The observed violation 2.291 +/- 0.008 not less, dbl equals1 clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden-variable theories.
An experimental demonstration of quantum contextuality with neutrons is presented, which intended to exhibit a Kochen-Specker-like phenomenon. Since no perfect correlation is expected in practical experiments, inequalities are derived to distinguish quantitatively the obtained results from predictions by a noncontextual hidden variable theory. Experiments were accomplished with the use of a neutron interferometer combined with spinor manipulation devices. The results clearly violate the prediction of noncontextual theories.
Neutron optical experiments are presented, which exhibit quantum contextual phenomena. Entanglement is achieved not between particles, but between degrees of freedom, in this case, for a single‐particle. Appropriate combinations of the direction of spin analysis and the position of the phase shifter allow an experimental verification of the violation of a Bell‐like inequality. Our experiments manifest the fact that manipulation of the wavefunction in one Hilbert space influences the result of the measurement in the other Hilbert space: manipulation without touch! Next, we report another experiment which exhibits other peculiarity of quantum contextuality, e.g., originally intended to show a Kochen‐Specker‐like phenomenon. We have introduced inequalities for quantitative analysis of the experiments. The value obtained in the experiments clearly showed violations of prediction by non‐contextual theory. Finally, we have accomplished a tomographic determination of entangled quantum state in single‐neutrons. There, characteristics of the Bell‐sate are confirmed: four poles for the real part of the density matrix are clearly seen.
Contextuality provides one of the fundamental characterizations of quantum phenomena, and can be used as a resource in lots of quantum information processing. In this paper, we summarize and derive some equivalent noncontextual inequalities from different noncontextual models of the proofs for the Kochen-Specker theorem based on Greenberger-Horne-Zeilinger states. These noncontextual inequalities are equivalent up to some correlation items which hold both for noncontextual hidden variable theories and quantum mechanics. Therefore, using single-photon hyperentangled Greenberger-Horne-Zeilinger states encoded by spin, path, and orbital angular momentum, we experimentally verify several state-dependent noncontextual models of the proofs for the Kochen-Specker theorem by testing an extreme simplest Mermin-like inequality.