  We re-examine the CHSH experiment, which we abstract here as a multi-round
game played between two parties with each party reporting a single binary
outcome at each round. We explore in particular the role that symmetries, and
the spontaneous breaking thereof, play in determining the maximally achievable
correlations between the two parties. We show, with the help of an explicit
statistical model, that the spontaneous breaking of rotational symmetry allows
for stronger correlations than those that can be achieved in its absence. We
then demonstrate that spontaneous symmetry breaking may lead to a violation of
the renowned CHSH inequality. We believe that the ideas presented in this paper
open the door to novel research avenues that have the potential to deepen our
understanding of the quantum formalism and the physical reality that it
describes.
