Holographic AME states in black hole interiors

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 $n$-th Renyi entropies for any bi-partite 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 non-isometric holographic codes.