  We study the reconstruction of the bulk operators in AdS/CFT when the
geometry contains a black hole. The black hole exterior can be mapped to the
CFT via a very simple Petz map which coincides with the HKLL map reconstruction
of the black hole exterior. For the interior modes of the bulk theory, using
the definition of the Petz recovery channel in modular theory, we can find the
mapping from the black hole interior to the dual boundary theory. In the case
of the evaporating black hole, it is expected that the interior modes map to
some operators which have support only on the bath system, the cavity that
absorbs the Hawking radiation. The most important observation that we have here
is that in the case that we have a typical black hole microstate in the bulk,
the CFT dual of the interior modes that we can find using the Petz recovery
channel are exactly the operators which so-called "mirror operator " in the
Papadodimas-Raju proposal. Therefore, we can interpret Papadodimas-Raju
proposal as an example of the Petz map reconstruction. It may help us answer
some open questions about their procedure.
