Black Hole Entanglement and Quantum Error Correction

TL;DR

This paper develops a holographic, quantum error correction-based framework for describing black hole evaporation and interior reconstruction, addressing entanglement issues and the firewall transition.

Contribution

It introduces a practical, unitary evolution model with horizon degrees of freedom modeled as a finite entropy quantum system, utilizing quantum error correction for interior reconstruction.

Findings

Reconstruction of black hole interior using quantum error correction.

Framework clarifies the black hole final state proposal.

Analyzes transition to the firewall regime in maximally mixed states.

Abstract

It was recently argued by Almheiri et al that black hole complementarity strains the basic rules of quantum information theory, such as monogamy of entanglement. Motivated by this argument, we develop a practical framework for describing black hole evaporation via unitary time evolution, based on a holographic perspective in which all black hole degrees of freedom live on the stretched horizon. We model the horizon as a unitary quantum system with finite entropy, and do not postulate that the horizon geometry is smooth. We then show that, with mild assumptions, one can reconstruct local effective field theory observables that probe the black hole interior, and relative to which the state near the horizon looks like a local Minkowski vacuum. The reconstruction makes use of the formalism of quantum error correcting codes, and works for black hole states whose entanglement entropy does not yet saturate the Bekenstein-Hawking bound. Our general framework clarifies the black hole final state proposal, and allows a quantitative study of the transition into the "firewall" regime of maximally mixed black hole states.