# Dynamics of Entanglement Wedge Cross Section from Conformal Field Theories

## TL;DR

This paper investigates the dynamics of the entanglement wedge cross section in 2D holographic CFTs following a local operator quench, highlighting the role of classical correlations in subregion duality.

## Contribution

It derives the entanglement wedge cross section dynamics directly from CFTs using reflected entropy and compares it with mutual information, extending understanding of mixed state correlations.

## Key findings

- Reflected entropy dynamics match entanglement wedge cross section behavior.
- Classical correlations are significant in subregion duality during dynamical processes.
- Results are consistent for odd entanglement entropy, another mixed state measure.

## Abstract

We derive dynamics of the entanglement wedge cross section directly from the two-dimensional holographic CFTs with a local operator quench. This derivation is based on the reflected entropy, a correlation measure for mixed states. We further compare these results with the mutual information and ones for RCFTs. Our results directly suggest the classical correlation also plays an important role in the subregion/subregion duality even for dynamical setup. Besides a local operator quench, we study the reflected entropy in a heavy state and provide improved bulk interpretation. We checked the above results also hold for the odd entanglement entropy, which is another measure for mixed states related to the entanglement wedge cross section.