Classical limits and quantum advantage in nonlocal games
Chunxiao Liu (LPS)
We introduce nonlocal games, which are multiplayer games in which players must coordinate their answers to local questions to win, without communicating with each other. They can win more often when they are allowed to share an entangled quantum state (quantum strategy) than when they are not (classical strategy). This advantage of quantum strategies reveals correlations that cannot be explained by consistent, predetermined local answers—a manifestation of quantum contextuality. In this talk, I will introduce such games for stabilizer states and quantify their advantage by bounding the optimal classical winning probability. Using classical coding theory and statistical mechanics, we derive rigorous bounds and characterize its asymptotic behavior for the 1D cluster state and the 2D toric code. For cluster states, contextuality can be witnessed even when the global state-preparation fidelity decreases exponentially with system size. These results provide scalable tests of many-body quantum correlations, with applications to benchmarking quantum state preparation.