Quantum strong cosmic censorship and black hole evaporation

It is common folklore that semiclassical arguments suggest that in black hole evaporation an initially pure state can become mixed. This is known as the \emph{information loss puzzle} (or {\it paradox}). Here we argue that, if taken at face value, semiclassical gravity suggests the formation of a final singularity instead of information loss. A quantum strong cosmic censorship conjecture, for which we give a rigorous statement, supports this conclusion. Thus, there are no reasons to expect a failure of unitarity in black hole evaporation or for any quantum gravity theory that can `cure' singularities.