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Entanglement Wedge Reconstruction via Universal Recovery Channels

Cotler, Jordan and Hayden, Patrick and Penington, Geoffrey and Salton, Grant and Swingle, Brian and Walter, Michael (2019) Entanglement Wedge Reconstruction via Universal Recovery Channels. Physical Review X, 9 (3). Art. No. 031011. ISSN 2160-3308. doi:10.1103/PhysRevX.9.031011.

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In the context of quantum theories of spacetime, one overarching question is how quantum information in the bulk spacetime is encoded holographically in boundary degrees of freedom. It is particularly interesting to understand the correspondence between bulk subregions and boundary subregions in order to address the emergence of locality in the bulk quantum spacetime. For the AdS/CFT correspondence, it is known that this bulk information is encoded redundantly on the boundary in the form of an error-correcting code. Having access only to a subregion of the boundary is as if part of the holographic code has been damaged by noise and rendered inaccessible. In quantum-information science, the problem of recovering information from a damaged code is addressed by the theory of universal recovery channels. We apply and extend this theory to address the problem of relating bulk and boundary subregions in AdS/CFT, focusing on a conjecture known as entanglement wedge reconstruction. Existing work relies on the exact equivalence between bulk and boundary relative entropies, but these are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. We show that the framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture as well as new physical insights. Most notably, we find that a bulk operator acting in a given boundary region’s entanglement wedge can be expressed as the response of the boundary region’s modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes’s rule that attempts to undo the noise induced by restricting to only a portion of the boundary. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra.

Item Type:Article
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Penington, Geoffrey0000-0002-8627-5237
Additional Information:© 2019 Published by the American Physical Society. 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 15 October 2018; revised manuscript received 11 February 2019; published 24 July 2019. We thank Mario Berta, Tom Faulkner, Daniel Harlow, Eliot Hijano, Aitor Lewkowycz, Sepehr Nezami, Jonathan Oppenheim, David Sutter, Mark Van Raamsdonk, and Mark Wilde for helpful discussions and feedback. BGS is supported by the Simons Foundation’s It from Qubit Collaboration, through a Simons Investigator grant to Senthil Todadri and by Multidisciplinary University Research Initiatives (MURI) Grant No. W911NF-14-1-0003 from ARO. G. S. is grateful to Canada’s NSERC for a postgraduate scholarship, and to the IQIM at Caltech and the SITP at Stanford. M.W. and P. H. gratefully acknowledge support from the Simons Foundation’s Investigator program and It from Qubit Collaboration, as well as AFOSR Grant No. FA9550-16-1-0082. P. H. is also supported by CIFAR. M.W. also acknowledges financial support from the NWO through Veni Grant No. 680-47-459.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Army Research Office (ARO)W911NF-14-1-0003
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Stanford UniversityUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
Canadian Institute for Advanced Research (CIFAR)UNSPECIFIED
Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)UNSPECIFIED
Subject Keywords:Gravitation, Quantum Information, String Theory
Issue or Number:3
Record Number:CaltechAUTHORS:20190724-150856685
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97390
Deposited By: Tony Diaz
Deposited On:24 Jul 2019 22:26
Last Modified:16 Nov 2021 17:31

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