Contextuality as a signature of quantum chaos

Quantum chaos is the study of quantum systems which exhibit chaotic dynamics in some classical limit. While classical chaos can be characterized by the Lyapunov exponent - the rate at which neighbouring trajectories diverge, a corresponding quantum characterization is difficult due to the linearity of quantum evolution and the uncertainty principle. Hence, one must identify features intrinsic to the quantum system which indicate the emergence of chaos in the classical limit. One such feature is contextuality, whereby quantum systems can generate measurement statistics which cannot be reproduced by any classical model. Here, we show that contextuality, as witnessed by violations of a Bell-type inequality, can capture the structure of the phase space for the classical kicked top, and is therefore a useful signature of chaos. Our results indicate that it is in fact the non-classicality of this quantum system which characterizes the emergence of chaos, and hence suggest a generalization of previously identified quantum signatures such as entanglement and coherence.