  We consider the generalized second law of black hole thermodynamics in the
light of quantum information theory, in particular information erasure and
Landauer's principle (namely, that erasure of information produces at least the
equivalent amount of entropy). A small quantum system outside a black hole in
the Hartle-Hawking state is studied, and the quantum system comes into thermal
equilibrium with the radiation surrounding the black hole. For this scenario,
we present a simple proof of the generalized second law based on quantum
relative entropy. We then analyze the corresponding information erasure
process, and confirm our proof of the generalized second law by applying
Landauer's principle.
