Approximate locality, black hole complementarity and overlapping qubits

We construct a toy model of an evaporating black hole using approximately local degrees of freedom acting on overlapping" qubits in which a version of black hole complementarity arises naturally. The operators corresponding to the radiation and the interior are identified as two distinct representations of the same fundamental algebra, thereby preventing the exact factorization of the Hilbert space into interior and exterior and avoiding the conventional no-cloning violations. We show how this toy model captures several qualitative and quantitative features of black hole evaporation and how the ability to account for this overlap" in the entropy calculation leads to the recovery of a Page curve.