# Comments on Entanglement Propagation

## TL;DR

This paper investigates how entanglement spreads in 2+1D holographic conformal field theories after a local quench, revealing an emergent lightcone with a distinct propagation speed and analyzing its relation to other velocities.

## Contribution

It extends previous work by characterizing the entanglement propagation speed and its relation to information and hydrodynamic velocities in strongly coupled theories.

## Key findings

- Entanglement propagates along an emergent lightcone with a distinct speed.
- Early-time entanglement velocities are close to the butterfly velocity.
- Late-time entanglement velocities for large regions are less regular.

## Abstract

We extend our work on entanglement propagation following a local quench in 2+1 dimensional holographic conformal field theories. We find that entanglement propagates along an emergent lightcone, whose speed of propagation $v_E$ seems distinct from other measures of quantum information spreading. We compare the relations we find to information and hydrodynamic velocities in strongly coupled 2+1 dimensional theories. While early-time entanglement velocities corresponding to small entangling regions are numerically close to the butterfly velocity, late-time entanglement velocities for large regions show less regularity. We also generalize and extend our previous results regarding the late-time decay of the entanglement entropy back to its equilibrium value.