The Page curve from the entanglement membrane

TL;DR

This paper demonstrates how the entanglement membrane framework explains the Page curve and information transfer in black hole models, linking quantum chaos with black hole information paradox resolutions.

Contribution

It introduces the entanglement membrane as a tool to derive the Page curve and analyze information transfer in toy black hole models, connecting quantum chaos with gravitational phenomena.

Findings

Page curve arises from a transition in the entanglement membrane at the Page time.

Information is rapidly transferred from black hole to radiation around the Page time.

The entanglement membrane approach parallels quantum extremal surface transitions in gravity.

Abstract

We study entanglement dynamics in toy models of black hole information built out of chaotic many-body quantum systems, by utilising a coarse-grained description of entanglement dynamics in such systems known as the `entanglement membrane'. We show that in these models the Page curve associated to the entropy of Hawking radiation arises from a transition in the entanglement membrane around the Page time, in an analogous manner to the change in quantum extremal surfaces that leads to the Page curve in semi-classical gravity. We also use the entanglement membrane prescription to study the Hayden-Preskill protocol, and demonstrate how information initially encoded in the black hole is rapidly transferred to the radiation around the Page time. Our results relate recent developments in black hole information to generic features of entanglement dynamics in chaotic many-body quantum systems.