The black hole interior from non-isometric codes and complexity
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13130_2024_Article_23775.pdf
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Author(s)
Akers, Chris
Engelhardt, Netta
Harlow, Daniel
Penington, Geoff
Vardhan, Shreya
Date Issued
June 24, 2024
Journal
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Citation
Akers, C., Engelhardt, N., Harlow, D. et al. The black hole interior from non-isometric codes and complexity. J. High Energ. Phys. 2024, 155 (2024).
Version
Final published version
Abstract
Quantum error correction has given us a natural language for the emergence of spacetime, but the black hole interior poses a challenge for this framework: at late times the apparent number of interior degrees of freedom in effective field theory can vastly exceed the true number of fundamental degrees of freedom, so there can be no isometric (i.e. inner-product preserving) encoding of the former into the latter. In this paper we explain how quantum error correction nonetheless can be used to explain the emergence of the black hole interior, via the idea of “non-isometric codes protected by computational complexity”. We show that many previous ideas, such as the existence of a large number of “null states”, a breakdown of effective field theory for operations of exponential complexity, the quantum extremal surface calculation of the Page curve, post-selection, “state-dependent/state-specific” operator reconstruction, and the “simple entropy” approach to complexity coarse-graining, all fit naturally into this framework, and we illustrate all of these phenomena simultaneously in a soluble model.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
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DOI of Published Version
https://doi.org/10.1007/jhep06(2024)155
