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Quantum error correcting codes with finite-dimensional Hilbert spaces haveyielded new insights on bulk reconstruction in AdS/CFT. In this paper, we givean explicit construction of a quantum error correcting code where the code andphysical Hilbert spaces are infinite-dimensional. We define a von Neumannalgebra of type II$_1$ acting on the code Hilbert space and show how it ismapped to a von Neumann algebra of type II$_1$ acting on the physical Hilbertspace. This toy model demonstrates the equivalence of entanglement wedgereconstruction and the exact equality of bulk and boundary relative entropiesin infinite-dimensional Hilbert spaces.

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