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 manybody 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 welldefined macroscopic geometry. When combined with the existing AdS/CFT error correction story, this shows that black holes are enormously robust against erasure errors.
 Authors:

 Berkeley Center for Theoretical Physics, Berkeley, CA (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 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 (SC21)
 OSTI Identifier:
 1566871
 Report Number(s):
 BNL2121362019JAAM
Journal ID: ISSN 10298479
 Grant/Contract Number:
 SC0012704
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Volume: 2019; Journal Issue: 8; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; AdSCFT 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.
Bao, Ning, & Cheng, Newton. Eigenstate thermalization hypothesis and approximate quantum error correction. United States. doi:10.1007/JHEP08(2019)152.
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.
@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 manybody 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 welldefined 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)},
issn = {10298479},
number = 8,
volume = 2019,
place = {United States},
year = {2019},
month = {8}
}
Figures / Tables:
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Figures / Tables found in this record: