Entanglement island, miracle operators and the firewall
In this paper, we obtain some general results on information retrieval from the black hole interior, based on the recent progress on quantum extremal surface formula and entanglement island. We study an AdS black hole coupled to a bath with generic dynamics, and ask whether it is possible to retrieve information about a small perturbation in the interior from the bath system. We show that the one-norm distance between two reduced states in a bath region A is equal to the same quantity in the bulk quantum field theory for region AI where I is the entanglement island of A. This is a straightforward generalization of bulk-boundary correspondence in AdS/CFT. However, we show that a contradiction arises if we apply this result to a special situation when the bath dynamics includes a unitary operation that carries a particular measurement to a region A and send the result to another region W. Physically, the contradiction arises between transferability of classical information during the measurement, and non-transferability of quantum information which determines the entanglement island. We propose that the resolution of the contradiction is to realize that the state reconstruction formula does not apply to the special situation involving interior-information-retrieving measurements. This implies that the assumption of smooth replica AdS geometry with boundary condition set by the flat space bath has to break down when the particular measurement operator is applied to the bath. Using replica trick, we introduce an explicitly construction of such operator, which we name as “miracle operators”. From this construction we see that the smooth replica geometry assumption breaks down because we have to introduce extra replica wormholes connecting with the “simulated blackholes” introduced by the miracle operator. We study the implication of miracle operators in understanding the firewall paradox.
- Research Organization:
- University of California, Oakland, CA (United States); Stanford University, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); Simons Foundation; National Science Foundation (NSF)
- Grant/Contract Number:
- SC0019380
- OSTI ID:
- 1976431
- Journal Information:
- Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 1 Vol. 2022; ISSN 1029-8479
- Publisher:
- Springer NatureCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Similar Records
Local measures of entanglement in black holes and CFTs
Including contributions from entanglement islands to the reflected entropy