Simulation of the Bell inequality violation based on quantum steering concept

Violation of Bell's inequality in experiments shows that predictions of local realistic models disagree with those of quantum mechanics. However, despite the quantum mechanics formalism, there are debates on how does it happen in nature. In this paper by use of a model of polarizers that obeys the Malus' law and quantum steering concept, i.e. superluminal influence of the states of entangled pairs to each other, simulation of phenomena is presented. The given model, as it is intended to be, is extremely simple without using mathematical formalism of quantum mechanics. However, the result completely agrees with prediction of quantum mechanics. Although it may seem trivial, this model can be applied to simulate the behavior of other not easy to analytically evaluate effects, such as deficiency of detectors and polarizers, different value of photons in each run and so on. For example, it is demonstrated, when detector efficiency is 83% the S factor of CHSH inequality will be 2, which completely agrees with famous detector efficiency limit calculated analytically. Also, it is shown in one-channel polarizers the polarization of absorbed photons, should change to the perpendicular of polarizer angle, at very end, to have perfect violation of the Bell inequality (2 root 2) otherwise maximum violation will be limited to (1.5 root 2).

Automated summary

This paper presents a simple model using Malus' law and quantum steering concept to simulate phenomena and show that it agrees with predictions of quantum mechanics. The model can be applied to simulate difficult to evaluate effects such as detector deficiencies and different photon values, providing insights into the behavior of these systems.