Khrennikov Andrei, Basieva Irina
International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, 351 95 Växjö, Sweden.
Prokhorov General Physics Institute, Vavilov str. 38D, 119991 Moscow, Russia.
Entropy (Basel). 2018 Apr 13;20(4):280. doi: 10.3390/e20040280.
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 CHSH = 2 2 to the classical bound C CHSH = 2 , i.e., F CHSH = Q CHSH C CHSH = 2 is less than the fraction of the quantum bound for the OB inequality Q OB = 3 2 to the classical bound C OB = 1 , i.e., F OB = Q OB C OB = 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.
本文的目的是吸引实验者关注被克劳泽 - 霍恩 - 希莫尼 - 霍尔特（CHSH）不等式的普遍讨论所掩盖的原始贝尔（OB）不等式。有两个理由去检验OB不等式而非CHSH不等式。首先，OB不等式是爱因斯坦 - 波多尔斯基 - 罗森（EPR）论证的直接结果。此外，只有这个不等式与EPR - 玻尔辩论直接相关。伊塔马尔·皮托夫斯基强调了OB不等式的第二个显著特征。他指出，与CHSH不等式相比，OB不等式对经典性的违背程度更高。对于CHSH不等式，量子（齐雷尔森）界限Q_CHSH = 2√2与经典界限C_CHSH = 2的比值，即F_CHSH = Q_CHSH / C_CHSH = √2小于OB不等式的量子界限Q_OB = 3√2与经典界限C_OB = 1的比值，即F_OB = Q_OB / C_OB = 3√2。因此，通过违背OB不等式，可以更接近更高程度的与经典性的偏离。主要问题在于OB不等式是在完美（反）关联的假设下推导出来的。然而，过去几年量子技术取得了惊人的发展。如今，可以以非常高的概率产生处于单重态光子对的源已经存在了。此外，光子探测器的效率也得到了极大提高。无论如何，可以从公平采样假设开始着手处理问题。另一种可能性是使用亨森等人关于纠缠电子的实验方案。在此方案中，探测效率非常高。
