HET Brown Bag | Non-isometric codes and the black hole interior

At late times, any holographic map from the large semiclassical Hilbert space in the interior of a black hole to the smaller Hilbert space in the boundary must be non-isometric. This implies that a large set of states in the bulk description do not exist in the fundamental description of the system. Despite this, I will show using a simple model that bulk states and operators whose complexity is sub-exponential in the black hole entropy can be represented in the boundary. I will also discuss the validity of the quantum extremal surface formula and entanglement wedge reconstruction for this non-isometric map.