Quantum error correction in the black hole interior

We will discuss the quantum error correction properties of the black hole interior in a toy model for an evaporating black hole in JT gravity entangled with a non-gravitational bath. After the Page time, the black hole interior degrees of freedom  in this system are encoded in the bath Hilbert space. We will use the gravitational path integral to show that the interior density matrix is correctable against the action of quantum operations on the bath which (i) do not have prior access to details of the black hole microstates, and (ii) do not have a large, negative coherent information with respect to the maximally mixed state on the bath, with the lower bound controlled by the black hole entropy and code subspace dimension. Thus, the encoding of the black hole interior in the radiation is robust against generic, low-rank quantum operations. In more general entanglement wedges, we expect similar, robust error correction in the ``python's lunch'' portion of the wedge, a manifestation of the complexity of the holographic encoding map in this region.