  We consider the time evolution of mixed state correlation measures in
two-dimensional conformal field theories, such as logarithmic negativity, odd
entropy, and reflected entropy, after quantum quenches of various kinds. These
correlation measures, in the holographic context, are all associated to the
entanglement wedge cross section. We contrast various classes of conformal
field theories, both rational and irrational (pure) conformal field theories.
First, for rational conformal field theories, whose dynamics can be well
described by the quasi-particle picture, we find all four quantities for
disjoint intervals to be proportional, regardless of the specific quench
protocol. Second, using the light cone bootstrap, we generalize our results to
irrational conformal field theories where we find sharp distinctions from the
quasi-particle results and striking differences between mutual information and
the other measures. The large surplus of logarithmic negativity relative to
mutual information forces us to reconsider what mutual information and
logarithmic negativity really measure. We interpret these results as a
signature of information scrambling and chaos in irrational theories. These CFT
results perfectly agree with our gravitational (holographic) calculations.
Furthermore, using holography, we are able to generalize the results to outside
of the light cone limit. Finally, due to the breakdown of the quasi-particle
picture for irrational theories, we appeal to the "line-tension picture,"
motivated by random unitary circuits, as a phenomenological description. We
observe that random unitary circuits, with local Hilbert space dimension
determined by the Cardy formula, have precisely the same entanglement dynamics
as irrational (including holographic) conformal field theories.
