Chaos and relative entropy

Understand

One characterization of a chaotic system is the quick delocalization of quantum information (fast scrambling).

• One therefore expects that in such a system a state quickly becomes locally indistinguishable from its perturbations.
• In this paper we study the time dependence of the relative entropy between the reduced density matrices of the thermofield double state and its perturbations in two dimensional conformal field theories.
• We show that in a CFT with a gravity dual, this relative entropy exponentially decays until the scrambling time.