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Code Properties from Holographic Geometries

Pastawski, Fernando and Preskill, John (2017) Code Properties from Holographic Geometries. Physical Review X, 7 (2). Art. No. 021022. ISSN 2160-3308. https://resolver.caltech.edu/CaltechAUTHORS:20170517-114206968

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Abstract

Almheiri, Dong, and Harlow [J. High Energy Phys. 04 (2015) 163.] proposed a highly illuminating connection between the AdS/CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here, we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes that admit a holographic interpretation. We introduce a new quantity called price, which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit uberholography, meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales that are small compared to the AdS curvature radius.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevX.7.021022DOIArticle
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.7.021022PublisherArticle
https://arxiv.org/abs/1612.00017arXivDiscussion Paper
Additional Information:© 2017 The Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Received 5 January 2017; published 15 May 2017. F. P. would like to thank Nicolas Delfosse, Henrik Wilming, and Jens Eisert for helpful discussions and comments. F. P. gratefully acknowledges funding provided by the Institute for Quantum Information and Matter, a NSF Physics Frontiers Center, with support from the Gordon and Betty Moore Foundation, as well as the Simons Foundation through the It from Qubit program and the FUB through the ERC project (TAQ). This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1125915.
Group:IQIM, Institute for Quantum Information and Matter
Funders:
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
NSF Physics Frontiers CenterUNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Simons Foundation309981
European Research Council (ERC)UNSPECIFIED
NSFPHY-1125915
Issue or Number:2
Record Number:CaltechAUTHORS:20170517-114206968
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170517-114206968
Official Citation:Code Properties from Holographic Geometries Fernando Pastawski and John Preskill Phys. Rev. X 7, 021022 (2017) – Published 15 May 2017
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77528
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:17 May 2017 19:20
Last Modified:03 Oct 2019 17:58

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