Entanglement Wedge Reconstruction of Infinite-dimensional von Neumann Algebras using Tensor Networks
arXiv:1910.06328 · doi:10.1103/PhysRevD.103.126018
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 acting on the code Hilbert space and show how it is mapped to a von Neumann algebra of type II 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.
51 pages + appendix, 4 figures
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- One-shot holography
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- Gauging the bulk: generalized gauging maps and holographic codes
- Holographic baby universes: an observable story
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- Deriving the non-perturbative gravitational dual of quantum Liouville theory from BCFT operator algebra
- On Infinite Tensor Networks, Complementary Recovery and Type II Factors
- Holographic Tensor Networks as Tessellations of Geometry