  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.
