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I was reading this paper "Quantum physics needs complex numbers" by Renou et al. In the paper, they propose the standard entanglement swapping scenario and use CHSH3 inequality to show that the maximal bound predicted by quantum mechanics can't be achieved. I have two questions regarding this

Why did the authors use the CHSH3 inequality instead of the CHSH inequality. Real quantum mechanics should also not be achieve maximal violation of CHSH so why CHSH3?

Also is there a more intuitive explanation for why the reall simulation fails in the entanglement swapping scenario but works fine in the Bell experiment scenario? The authors do provide a reason but I didn't quite find it so intuitive)

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    $\begingroup$ I would suggest adding a brief explanation of what the CHSH$_3$ inequality (as given in the paper) and quoting the related text rather than expecting people to read the entire paper to find what you mention. $\endgroup$
    – StephenG - Help Ukraine
    Commented Apr 4, 2021 at 8:51
  • $\begingroup$ I second the above comment. As it is written now, it is not even clear what "real quantum mechanics" is. $\endgroup$
    – Norbert Schuch
    Commented Apr 4, 2021 at 13:42
  • $\begingroup$ Of course real QM achieves maximum violation in CHSH. Where would you need complex numbers? $\endgroup$
    – Norbert Schuch
    Commented Apr 4, 2021 at 13:59

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