Black hole entanglement and quantum error correction

• Published in: The journal of high energy physics Vol. 2013; no. 10; pp. 1 - 34
• Main Authors: Verlinde, Erik, Verlinde, Herman
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2013; Springer Nature B.V
• Subjects: Black holes (astronomy); Classical and Quantum Gravitation; Elementary Particles; Entanglement; Entropy; Firewalls; High energy physics; Horizon; Information theory; Mathematical analysis; Mathematical models; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Reconstruction; Relativity Theory; String Theory; Statistical Methods; Black Holes
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2013)107

A
bstract
It was recently argued in [
1
] 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.