Contextuality and Chaos

Abstract: Classical chaos is marked by an extreme sensitivity to initial conditions, where infinitesimally close trajectories separate exponentially over time. In quantum mechanics, however, unitary evolution and the uncertainty principle preclude such behavior, necessitating alternative approaches to identifying chaos in quantum systems. One must therefore seek quantum features that can indicate the emergence of chaos in the classical limit. Here, we show that contextuality, a quantum property that defies classical explanations, can serve as a signature of chaos. For a spin system undergoing chaotic dynamics, we demonstrate that violations of Bell-type inequality can effectively differentiate regular and chaotic regions of the phase space, suggesting that the nonclassicality of the system underpins signatures of chaos.