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arXiv:quant-ph/0206070

The magic squares and Bell's theorem

P. K. Aravind

Published Jun 11, 2002• 22 citations
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Abstract

This paper describes a device, consisting of a central source and two widely separated detectors with six switch settings each, that provides a simple gedanken demonstration of quantum nonlocality suitable for a general audience. A comparison is made with several earlier gedanken demonstrations of the same type given by Mermin, and the new features of the present scheme are highlighted.

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This paper describes a device, consisting of a central source and two widely
separated detectors with six switch settings each, that provides a simple
gedanken demonstration of quantum nonlocality suitable for a general audience.
A comparison is made with several earlier gedanken demonstrations of the same
type given by Mermin, and the new features of the present scheme are
highlighted.
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".
A few years ago I described a simple device that reveals in a very elementary way the extremely perplexing character the data from the Bohm–Einstein–Podolsky–Rosen experiment assumes in the light of the analysis of J. S. Bell. There is a second, closely related form of that gedanken demonstration, which I would like to examine for several reasons. It is simpler: there are only two (not three) settings for each switch. The gedanken data resemble more closely the data collected in actual realizations of the device. None of the possible switch settings produce the perfect correlations found in the first version of the gedanken demonstration, where the lights always flash the same color when the switches have the same setting. Since absolutely perfect correlations are never found in the imperfect experiments we contend with in the real world, an argument that eliminates this feature of the ideal gedanken data can be applied to real data from real experiments. (If you believe, however, along with virtually all physicists, that the quantum theory gives the correct ideal limiting description of all phenomena to which it can be applied, then this is not so important a consideration.) Because the ideal perfect correlations are absent from this version of the gedanken demonstration, one is no longer impelled to assert the existence of impossible instruction sets. To establish that the new data nevertheless remain peculiar, it is necessary to take a different line of attack, which has again intriguing philosophical implications, but of a rather different character. The modified demonstration In the modified gedanken demonstration there are only two switch settings (1 and 2) at each detector.
A logic circuit is used to light bulbs in accordance with quantum predictions and in violation of the predictions of a local realistic theory. This makes Mermin’s gedanken experiment, in which the Einstein–Podolsky–Rosen paradox (as sharpened by Bell) is presented with the minimum of technicalities, a feasible and instructive lecture demonstration. We give circuit details, a useful order of presentation, the reactions of a class of nonscience majors, and a simple general proof of the incompatibility.