skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

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]
  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
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.
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 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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Bulk locality and quantum error correction in AdS/CFT
journal, April 2015

  • Almheiri, Ahmed; Dong, Xi; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2015, Issue 4
  • DOI: 10.1007/JHEP04(2015)163

The Ryu–Takayanagi Formula from Quantum Error Correction
journal, May 2017


Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

  • Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel
  • Journal of High Energy Physics, Vol. 2015, Issue 6
  • DOI: 10.1007/JHEP06(2015)149

Black hole entanglement and quantum error correction
journal, October 2013

  • Verlinde, Erik; Verlinde, Herman
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)107

A Decoupling Approach to the Quantum Capacity
journal, March 2008

  • Hayden, Patrick; Horodecki, Michał; Winter, Andreas
  • Open Systems & Information Dynamics, Vol. 15, Issue 01
  • DOI: 10.1142/S1230161208000043

Random Quantum Codes from Gaussian Ensembles and an Uncertainty Relation
journal, March 2008

  • Hayden, Patrick; Shor, Peter W.; Winter, Andreas
  • Open Systems & Information Dynamics, Vol. 15, Issue 01
  • DOI: 10.1142/S1230161208000079

Chaos in quantum channels
journal, February 2016

  • Hosur, Pavan; Qi, Xiao-Liang; Roberts, Daniel A.
  • Journal of High Energy Physics, Vol. 2016, Issue 2
  • DOI: 10.1007/JHEP02(2016)004

From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
journal, May 2016


Eigenstate thermalization hypothesis
journal, July 2018


Subsystem eigenstate thermalization hypothesis
journal, January 2018


Universality of quantum information in chaotic CFTs
journal, March 2018

  • Lashkari, Nima; Dymarsky, Anatoly; Liu, Hong
  • Journal of High Energy Physics, Vol. 2018, Issue 3
  • DOI: 10.1007/JHEP03(2018)070

Recoverability in quantum information theory
journal, October 2015

  • Wilde, Mark M.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 471, Issue 2182
  • DOI: 10.1098/rspa.2015.0338

Typicality and thermality in 2d CFT
journal, July 2019

  • Datta, Shouvik; Kraus, Per; Michel, Ben
  • Journal of High Energy Physics, Vol. 2019, Issue 7
  • DOI: 10.1007/JHEP07(2019)143

Hot halos and galactic glasses (carbonado)
journal, January 2012

  • Anninos, Dionysios; Anous, Tarek; Barandes, Jacob
  • Journal of High Energy Physics, Vol. 2012, Issue 1
  • DOI: 10.1007/JHEP01(2012)003

Supergoop dynamics
journal, March 2013

  • Anninos, Dionysios; Anous, Tarek; Denef, Frederik
  • Journal of High Energy Physics, Vol. 2013, Issue 3
  • DOI: 10.1007/JHEP03(2013)081

Holographic vitrification
journal, April 2015

  • Anninos, Dionysios; Anous, Tarek; Denef, Frederik
  • Journal of High Energy Physics, Vol. 2015, Issue 4
  • DOI: 10.1007/JHEP04(2015)027

Eigenstate thermalization in the Sachdev-Ye-Kitaev model
journal, November 2017


Phases of scrambling in eigenstates
journal, January 2019