Eigenstate thermalization hypothesis and approximate quantum error correction

Bao, Ning; Cheng, Newton

doi:10.1007/JHEP08(2019)152

Title: Eigenstate thermalization hypothesis and approximate quantum error correction

Journal Article · 27 August 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP08(2019)152 · OSTI ID:1566871

Bao, Ning ^[1]; Cheng, Newton ^[2]

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)

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.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (SC-21)

Grant/Contract Number:: SC0012704

OSTI ID:: 1566871

Report Number(s):: BNL--212136-2019-JAAM

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 8 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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