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Entanglement wedge reconstruction of infinite-dimensional von Neumann algebras using tensor networks

Kang, Monica Jinwoo and Kolchmeyer, David K. (2021) Entanglement wedge reconstruction of infinite-dimensional von Neumann algebras using tensor networks. Physical Review D, 103 (12). Art. No. 126018. ISSN 2470-0010. doi:10.1103/PhysRevD.103.126018.

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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 II₁ acting on the code Hilbert space and show how it is mapped to a von Neumann algebra of type II₁ 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:Article
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URLURL TypeDescription Paper
Kang, Monica Jinwoo0000-0002-0454-2064
Kolchmeyer, David K.0000-0002-4973-9848
Additional Information:© 2021 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. Funded by SCOAP3. Received 31 July 2020; accepted 15 May 2021; published 17 June 2021. 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 No DE-SC0011632. D. K. would like to acknowledge a partial support from NSF Grant No. PHY-1352084.
Group:Walter Burke Institute for Theoretical Physics
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Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
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Issue or Number:12
Record Number:CaltechAUTHORS:20191028-153035644
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99513
Deposited By: Joy Painter
Deposited On:28 Oct 2019 22:58
Last Modified:21 Jun 2021 23:22

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