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 to the classical bound i.e., is less than the fraction of the quantum bound for the OB inequality to the classical bound i.e., 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.
Highlights
In his paper [1], Bell proposed the probabilistic test based on the EPR-argument [3].The problem under consideration can be formulated as follows
Podolsky, and Rosen proved that quantum mechanics (QM) is incomplete, since its formalism does not represent the EPR elements of reality
Under the assumptions of 100% perfect anti-correlations and set-independent joint detection efficiency (see (17)), the following original Bell (OB) inequality for detectable correlations holds:
Summary
In his paper [1] (see [2]), Bell proposed the probabilistic test based on the EPR-argument [3]. For the singlet state, subquantum and quantum correlations can be identified (see Appendixes B and C for further discussion) This beautiful theoretical scheme supporting nonlocal hidden variable theories did not match the experimental framework of that time, since the degree of (anti-)correlations (for the same setting on both sides) was not so high. This problem was solved by transition from the OB inequality to the CHSH inequality [4] or the similar inequalities: the CH74 inequality [5,6] or the Eberhard inequality [7] (see [8] for comparison of these inequalities). Successful experimental testing of violation of the OB inequality would be an important ( very challenging) contribution to clarification of quantum foundations
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