# Towards Experiments to Test Violation of the Original Bell Inequality

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International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, 351 95 Växjö, Sweden

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Prokhorov General Physics Institute, Vavilov str. 38D, 119991 Moscow, Russia

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Department of Psychology, University of London, London WC1E 7HU, UK

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Author to whom correspondence should be addressed.

Received: 16 February 2018 / Revised: 29 March 2018 / Accepted: 11 April 2018 / Published: 13 April 2018

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

# Abstract

The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser–Horne–Shimony–Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein–Podolsky–Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR–Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound ${Q}_{\mathrm{CHSH}}=2\sqrt{2}$ to the classical bound ${C}_{\mathrm{CHSH}}=2,$ i.e., ${F}_{\mathrm{CHSH}}=\frac{{Q}_{\mathrm{CHSH}}}{{C}_{\mathrm{CHSH}}}=\sqrt{2}$ is less than the fraction of the quantum bound for the OB inequality ${Q}_{\mathrm{OB}}=\frac{3}{2}$ to the classical bound ${C}_{\mathrm{OB}}=1,$ i.e., ${F}_{\mathrm{OB}}=\frac{{Q}_{\mathrm{OB}}}{{C}_{\mathrm{OB}}}=\frac{3}{2}.$ Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high. View Full-Text
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**MDPI and ACS Style**

Khrennikov, A.; Basieva, I. Towards Experiments to Test Violation of the Original Bell Inequality. *Entropy* **2018**, *20*, 280.

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