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arXiv · 1910.06328

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

Monica Jinwoo Kang·David K. Kolchmeyer
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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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Monica Jinwoo Kang, David K. Kolchmeyer. 2019-10-14. Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks. https://doi.org/10.1103/physrevd.103.126018

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