  We derive dynamics of the entanglement wedge cross section from the reflected
entropy for local operator quench states in the holographic CFT. By comparing
between the reflected entropy and the mutual information in this dynamical
setup, we argue that (1) the reflected entropy can diagnose a new perspective
of the chaotic nature for given mixed states and (2) it can also characterize
classical correlations in the subregion/subregion duality. Moreover, we point
out that we must improve the bulk interpretation of a heavy state even in the
case of well-studied entanglement entropy. Finally, we show that we can derive
the same results from the odd entanglement entropy. The present paper is an
extended version of our earlier report arXiv:1907.06646 and includes many new
results: non-perturbative quantum correction to the reflected/odd entropy,
detailed analysis in both CFT and bulk sides, many technical aspects of replica
trick for reflected entropy which turn out to be important for general setup,
and explicit forms of multi-point semi-classical conformal blocks under
consideration.
