The CHSH Game, Tsirelson's Bound, and Causal Locality

We reformulate the CHSH game in terms of indivisible stochastic processes. Using Barandes’s stochastic-quantum correspondence and its associated definition of causal locality, we present a novel proof of the Tsirelson bound. In particular, we show that unlike the no-signaling principle alone, the postulates defining causally local, indivisible stochastic processes are precisely strong enough to allow for violations of the Bell inequality up to, but not beyond, the Tsirelson bound.