Contextuality quantification and self-testing in many-body quantum systems via nonlocal games

Contextuality is the fundamental property that makes quantum mechanics different from classical physics. It is responsible for quantum computational speedups in both magic-state-injection-based and measurement-based models of computation, and can be probed directly in a many-body setting by multiplayer nonlocal quantum games. In this talk, we discuss a family of games that can be won with certainty when a CSS codeword is shared by the players and introduce an efficient, many-body-physics-inspired method for computing the optimal classical win probability, which serves as a direct probe of the shared state's contextuality. This method reveals direct connections between, e.g., the contextuality of single-site Pauli measurements in a toric code state, the partition function of a zero-temperature antiferromagnetic Potts model, and strange correlators in symmetry-protected topological states. Finally, we show how a slight modification of these games enables a translation-invariant protocol that self-tests many-body quantum states.