We argue that the special extremal slice inside an AdS black hole is dual to an absolutely maximally entangled (AME) state. We demonstrate this by confirming the n-independence of holographic nth Renyi entropies for any bipartite subsystems. Our result gives an AME state in an infinite-volume system, where the local bond dimension is set by the black hole entropy. In particular, our construction provides concrete support from the gravity side for the emergence of random structures and an infinite-dimensional Hilbert space in recent nonisometric holographic codes.
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
II1 acting on the code Hilbert space and show how it is mapped to a von Neumann algebra of type
II1 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.