Code Properties from Holographic Geometries
- Creators
- Pastawski, Fernando
-
Preskill, John
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.
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.Attached Files
Published - PhysRevX.7.021022.pdf
Submitted - 1612.00017.pdf
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Additional details
- Eprint ID
- 77528
- Resolver ID
- CaltechAUTHORS:20170517-114206968
- Institute for Quantum Information and Matter (IQIM)
- NSF Physics Frontiers Center
- Gordon and Betty Moore Foundation
- Simons Foundation
- 309981
- European Research Council (ERC)
- NSF
- PHY-1125915
- Created
-
2017-05-17Created from EPrint's datestamp field
- Updated
-
2021-11-15Created from EPrint's last_modified field
- Caltech groups
- Institute for Quantum Information and Matter