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Eigenstate thermalization hypothesis and approximate quantum error correction

  • Regular Article - Theoretical Physics
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  • Published: 27 August 2019
  • volume 2019, Article number: 152 (2019)
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Eigenstate thermalization hypothesis and approximate quantum error correction
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  • Ning Bao1,2 &
  • Newton Cheng1 
  • 663 Accesses

  • 6 Citations

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A preprint version of the article is available at arXiv.

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.

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Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Authors and Affiliations

  1. Berkeley Center for Theoretical Physics, Berkeley, CA, 94720, U.S.A.

    Ning Bao & Newton Cheng

  2. Computational Science Initiative, Brookhaven National Lab, Upton, NY, 11973, U.S.A.

    Ning Bao

Authors
  1. Ning Bao
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  2. Newton Cheng
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Corresponding author

Correspondence to Newton Cheng.

Additional information

ArXiv ePrint: 1906.03669

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Cite this article

Bao, N., Cheng, N. Eigenstate thermalization hypothesis and approximate quantum error correction. J. High Energ. Phys. 2019, 152 (2019). https://doi.org/10.1007/JHEP08(2019)152

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  • Received: 25 June 2019

  • Accepted: 14 August 2019

  • Published: 27 August 2019

  • DOI: https://doi.org/10.1007/JHEP08(2019)152

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Keywords

  • AdS-CFT Correspondence
  • Black Holes in String Theory
  • Conformal Field Theory
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