Reliable computation from contextual correlations

An operational approach to the study of computation based on correlations considers black boxes with one-bit inputs and outputs, controlled by a limited classical computer capable only of performing sums modulo-two. In this setting, it was shown that noncontextual correlations do not provide any extra computational power, while contextual correlations were found to be necessary for the deterministic evaluation of nonlinear Boolean functions. Here we investigate the requirements for reliable computation in this setting; that is, the evaluation of any Boolean function with success probability bounded away from $1/2$. We show that bipartite CHSH quantum correlations suffice for reliable computation. We also prove that an arbitrarily small violation of a multipartite Greenberger–Horne–Zeilinger noncontextuality inequality also suffices for reliable computation.