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arXiv:quant-ph/0104138

Mermin's pentagram and Bell's theorem

P. K. Aravind

Published Apr 30, 2001• 2 citations
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Abstract

It is shown how a proof of the Bell-Kochen-Specker (BKS) theorem given by Kernaghan and Peres can be experimentally realized using a scheme of measurements derived from a related proof of the same theorem by Mermin. It is also pointed out that if this BKS experiment is carried out independently by two distant observers who repeatedly make measurements on a specially correlated state of six qubits, it provides an inequality-free demonstration of Bell's theorem as well.

DOI
10.48550/arxiv.quant-ph/0104138

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In the Greenberger-Horne-Zeilinger-Mermin (GHZM) proof of Bell's theorem, a source periodically emits an entangled state of three particles whose properties are analyzed by three distant observers and used to prove Bell's nonlocality theorem. This paper analyzes a somewhat different gedanken experiment involving only two observers that nevertheless makes indirect use of the GHZ states to prove Bell's theorem. The relationship of the GHZM proof to the present one is discussed, and it is pointed out that the latter provides an interesting new view of the connection between the "two theorems of John Bell".
We show that an experimental demonstration of quantum contextuality using 2 degrees of freedom of single neutrons based on a violation of an inequality derived from the Peres-Mermin proof of the Kochen-Specker theorem would be more conclusive than those obtained from previous experiments involving pairs of ions [M. A. Rowe, Nature (London) 409, 791 (2001)10.1038/35057215] and single neutrons [Y. Hasegawa, Nature (London) 425, 45 (2003)10.1038/nature01881] based on violations of Clauser-Horne-Shimony-Holt-like inequalities.
A recent proof of Bell's theorem without inequalities [A. Cabello, Phys. Rev. Lett. 86, 1911 (2001)] is formulated as a Greenberger-Horne-Zeilinger-type proof involving just two observers. On one hand, this new approach allows us to derive an experimentally testable Bell inequality which is violated by quantum mechanics. On the other hand, it leads to a new state-independent proof of the Kochen-Specker theorem and provides a wider perspective on the relations between the major proofs of no hidden variables.