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

Authors
  • Jinwoo Kang, Monica
  • Kolchmeyer, David K.
Publication Date
Oct 14, 2019
Source
INSPIRE-HEP
Keywords
License
Unknown
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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.

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