TY - JOUR
T1 - Black hole entanglement and quantum error correction
AU - Verlinde, Erik
AU - Verlinde, Herman
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2013/10
Y1 - 2013/10
N2 - 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.
AB - 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.
KW - Black holes
KW - Statistical methods
UR - http://www.scopus.com/inward/record.url?scp=84892693041&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84892693041&partnerID=8YFLogxK
U2 - 10.1007/JHEP10(2013)107
DO - 10.1007/JHEP10(2013)107
M3 - Article
AN - SCOPUS:84892693041
VL - 2013
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 10
M1 - 107
ER -