Quantum chaos and macroscopic realism as no-signaling in time

Macroscopic realism is a set of assumptions about how we experience the world at a classical level. While the Leggett-Garg inequalities are temporal correlations that are violated by quantum systems not obeying such macrorealism, the no-signaling in time condition is also a necessary condition. This compares measurement outcomes with and without prior measurements. As dynamics and correlations play a central role in these measures, this paper explores the effects of regular versus chaotic dynamics on the violations of macroscopic realism. We observe a close connection between a 3 point out-of-time-order correlator and the conditional probabilities of measurement, and we find unmistakable imprints of chaos on the violations of macrorealism. We provide qualitative semiclassical reasoning for the numerical results involving a kicked top, and for two important initial states that behave very differently.