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I understood the CHSH game correlations by watching Prof. Vazirani's video. I also understood that the correlation between two measures taken from different basis are related by the cosine of the angle between the basis vectors (usually called $\theta$).

Now, when I watch other videos about the CHSH game (example) when it comes to the moment of calculating the correlations between measurements, it is used $\frac{\theta}{2}$.

Why is that?

FDGod
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