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Title: Eigenstate thermalization hypothesis and approximate quantum error correction

Abstract

The eigenstate thermalization hypothesis (ETH) is a powerful conjecture for understanding how statistical mechanics emerges in a large class of many-body quantum systems. It has also been interpreted in a CFT context, and, in particular, holographic CFTs are expected to satisfy ETH. Recently, it was observed that the ETH condition corresponds to a necessary and sufficient condition for an approximate quantum error correcting code (AQECC), implying the presence of AQECCs in systems satisfying ETH. In this paper, we explore the properties of ETH as an error correcting code and show that there exists an explicit universal recovery channel for the code. Based on the analysis, we discuss a generalization that all chaotic theories contain error correcting codes. We then specialize to AdS/CFT to demonstrate the possibility of total bulk reconstruction in black holes with a well-defined macroscopic geometry. When combined with the existing AdS/CFT error correction story, this shows that black holes are enormously robust against erasure errors.

Authors:
 [1];  [2]
+ Show Author Affiliations
  1. Berkeley Center for Theoretical Physics, Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
  2. Berkeley Center for Theoretical Physics, Berkeley, CA (United States)
Publication Date:
Research Org.:
Brookhaven National Lab. (BNL), Upton, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21)
OSTI Identifier:
1566871
Report Number(s):
BNL-212136-2019-JAAM
Journal ID: ISSN 1029-8479; TRN: US2001008
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2019; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; AdS-CFT Correspondence; Black Holes in String Theory; Conformal Field Theory

Citation Formats

Bao, Ning, and Cheng, Newton. Eigenstate thermalization hypothesis and approximate quantum error correction. United States: N. p., 2019. Web. doi:10.1007/JHEP08(2019)152.
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Bao, Ning, & Cheng, Newton. Eigenstate thermalization hypothesis and approximate quantum error correction. United States. doi:10.1007/JHEP08(2019)152.
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Bao, Ning, and Cheng, Newton. Tue . "Eigenstate thermalization hypothesis and approximate quantum error correction". United States. doi:10.1007/JHEP08(2019)152. https://www.osti.gov/servlets/purl/1566871.
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@article{osti_1566871,
title = {Eigenstate thermalization hypothesis and approximate quantum error correction},
author = {Bao, Ning and Cheng, Newton},
abstractNote = {The eigenstate thermalization hypothesis (ETH) is a powerful conjecture for understanding how statistical mechanics emerges in a large class of many-body quantum systems. It has also been interpreted in a CFT context, and, in particular, holographic CFTs are expected to satisfy ETH. Recently, it was observed that the ETH condition corresponds to a necessary and sufficient condition for an approximate quantum error correcting code (AQECC), implying the presence of AQECCs in systems satisfying ETH. In this paper, we explore the properties of ETH as an error correcting code and show that there exists an explicit universal recovery channel for the code. Based on the analysis, we discuss a generalization that all chaotic theories contain error correcting codes. We then specialize to AdS/CFT to demonstrate the possibility of total bulk reconstruction in black holes with a well-defined macroscopic geometry. When combined with the existing AdS/CFT error correction story, this shows that black holes are enormously robust against erasure errors.},
doi = {10.1007/JHEP08(2019)152},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2019,
place = {United States},
year = {2019},
month = {8}
}
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Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI:  10.1007/JHEP08(2019)152
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Cited by: 3 works
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Figures / Tables:

Figure 1 Figure 1: Given a subregion on the boundary, it can be uniquely associated to a dual spacetime region called the “entanglement wedge” of the subregion, as shown by the shaded region. An operator in the entanglement wedge, represented by a black dot, has a representation as an operator on themore » boundary. A larger boundary subregion (red) has an entanglement wedge that goes deeper into the bulk than a smaller one (blue). The operator at the center is well-protected against erasure errors on the boundary; it is unaffected by the deletion of the red or blue region.« less
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