  This paper illustrates the resemblance between the information-geometric
structures of probability spaces and that of the discrete spectrum for Hawking
radiation. The information geometry gives rise to a reconstruction of the
standard formalism of quantum mechanics, while the discrete spectrum of Hawking
radiation contributes to the semiclassical unitary evolution of Hawking
radiation. If more realistic models of Hawking radiation are chosen, the
information-geometric structures of the probability space for Hawking radiation
can be constructed from some physical considerations. The constructed quantum
formalism is consistent with both the unitary evolution of Hawking radiation in
the semiclassical picture and the topology change of fuzzy horizons. These
aspects of Hawking radiation can be connected to some general convictions of
quantum gravity. A comparison with the fuzzball proposal shows the limiation
and effectiveness of this construction. We conclude that these
information-geometric aspects show some possible ways bridging the gap between
semiclassical models and quantum gravity.
