  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. This decay is not uniform. We argue that the early time
exponent is universal while the late time exponent is sensitive to the
butterfly effect. This large $c$ answer breaks down at the scrambling time,
therefore we also study the relative entropy in a class of spin chain models
numerically. We find a similar universal exponential decay at early times,
while at later times we observe that the relative entropy has large revivals in
integrable models, whereas there are no revivals in non-integrable models.
