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Entanglement wedge reconstruction using the Petz map

Chen, Chi-Fang and Penington, Geoffrey and Salton, Grant (2020) Entanglement wedge reconstruction using the Petz map. Journal of High Energy Physics, 2020 (1). Art. No. 168. ISSN 1029-8479. doi:10.1007/jhep01(2020)168.

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At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension — no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Chen, Chi-Fang0000-0001-5589-7896
Penington, Geoffrey0000-0002-8627-5237
Additional Information:© 2020 The Author(s). 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. Article funded by SCOAP3. Received: November 5, 2019; Accepted: January 8, 2020; Published: January 28, 2020. We would like to thank Patrick Hayden, Richard Nally, and Michael Walter for valuable discussions. We would also like to thank Howard Barnum for insightful and stimulating conversation in the early stages of this project. CFC was supported by the Physics/Applied Physics/SLAC Summer Research Program for undergraduates at Stanford University. GP is supported by the Simons Foundation “It from Qubit" collaboration, AFOSR grant number FA9550-16-1-0082 and DOE award DE-SC0019. GS was supported by an IQIM postdoctoral fellowship at Caltech, DOE award Quantum Error Correction and Spacetime Geometry DE-SC0018407, the Simons Foundation "It from Qubit" collaboration, and by the Stanford Institute for Theoretical Physics.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Stanford UniversityUNSPECIFIED
Simons FoundationUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)FA9550-16-1-0082
Department of Energy (DOE)DE-SC0019
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Department of Energy (DOE)DE-SC0018407
Subject Keywords:AdS-CFT Correspondence; 1/N Expansion; Nonperturbative Effects
Issue or Number:1
Record Number:CaltechAUTHORS:20200129-105110731
Persistent URL:
Official Citation:Chen, CF., Penington, G. & Salton, G. J. High Energ. Phys. (2020) 2020: 168.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100984
Deposited By: Tony Diaz
Deposited On:29 Jan 2020 19:02
Last Modified:16 Nov 2021 17:58

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