Optimal bounds on the classical value of the repeated CHSH game

Abstract: We show that the maximum winning probability in the repeated CHSH game for classical strategies is at most $\left(\frac{1+\sqrt{5}}{4}\right)<sup>n$. Together with a matching lower bound by Barak et al. (FOCS'2008), this determines the asymptotic value of the repeated CHSH game exactly. We also show that, if an XOR game has a gap between classical and quantum values, there is also a gap between the asymptotic values for the repeated game.