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Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks

Kang, Monica Jinwoo and Kolchmeyer, David K. (2019) Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20191028-153035644

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Abstract

Quantum error correcting codes with finite-dimensional Hilbert spaces have yielded new insights on bulk reconstruction in AdS/CFT. In this paper, we give an explicit construction of a quantum error correcting code where the code and physical Hilbert spaces are infinite-dimensional. We define a von Neumann algebra of type II$_1$ acting on the code Hilbert space and show how it is mapped to a von Neumann algebra of type II$_1$ acting on the physical Hilbert space. This toy model demonstrates the equivalence of entanglement wedge reconstruction and the exact equality of bulk and boundary relative entropies in infinite-dimensional Hilbert spaces.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1910.06328arXivDiscussion Paper
Additional Information:The authors are grateful to Kai Xu for discussions and Daniel Harlow and Temple He for helpful comments on this paper. M.J.K. is supported by a Sherman Fairchild Postdoctoral Fellowship. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. D.K. would like to acknowledge a partial support from NSF grant PHY-1352084.
Group:Walter Burke Institute for Theoretical Physics
Funders:
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
NSFPHY-1352084
Sherman Fairchild FoundationUNSPECIFIED
Other Numbering System:
Other Numbering System NameOther Numbering System ID
CALT-TH2019-042
Record Number:CaltechAUTHORS:20191028-153035644
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20191028-153035644
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99513
Collection:CaltechAUTHORS
Deposited By: Joy Painter
Deposited On:28 Oct 2019 22:58
Last Modified:28 Oct 2019 22:58

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