# The experiment for testing the CHSH inequalities

I want to understand how an experiment is carried out to test violations of the CHSH inequalities. I read Wikipedia and one popular book on quantum mechanics. The Wikipedia article is too short and incomprehensible to me; in addition, the description from Wikipedia and from the book is different.

Wikipedia shows the following figure:

The figure in the book is the following:

In the book, the picture shows the waveplates in front of each PBS, and it says “these plates are set at angles 0, Pi/8, Pi/4 and 3Pi/8”. Wikipedia says “Four separate subexperiments are conducted, corresponding to the four terms E(a, b) in the test statistic S (2, above). The settings a, a′, b and b′ are generally in practice chosen to be 0, 45°, 22.5° and 67.5° respectively — the "Bell test angles" — these being the ones for which the quantum mechanical formula gives the greatest violation of the inequality”.

Thus, Wikipedia does not explain what are these angles 0, 45 °, etc., but the book says that these are the angles at which the waveplates are installed (and Wikipedia does not mention waveplates). So my question is, whether the waveplates are used in this experiment, and what do the angles at which they are installed mean?

I tried to read the original work of Clauser et al, there are no pictures and everything is not clear to me too. I ask you to advise popular sources that clearly describe the essence of the CHSH inequalities and the experiment to test them.

• Regarding the "essence of the CHSH inequalities": derivations and/or intuition about the inequality can be found in this post, this post, this post, this post, and probably others. Knowing what the angles mean doesn't matter for understanding how the inequality is derived or why it's important, but the last post cites a few experiment-references that might include some explanation of what the angles mean. Oct 16, 2021 at 23:11