  In a black hole, hair and quantum information retrieval are interrelated
phenomena. The existence of any new form of hair necessarily implies the
existence of features in the quantum-mechanically evaporated radiation.
Classical supertranslation hair can be only distinguished from global
diffeomorphisms if we have access to the interior of the black hole. Indirect
information on the interior can only be obtained from the features of the
quantum evaporation. Supertranslations $(T^-,T^+) \in BMS_{-}\otimes BMS_{+}$
can be used as bookkepers of the probability distributions of the emitted
quanta where the first element describes the classical injection of energy and
the second one is associated to quantum-mechanical emission. The connection
between $T^-$ and $T^+$ is determined by the interior quantum dynamics of the
black hole. We argue that restricting to the diagonal subgroup is only possible
for decoupled modes, which do not bring any non-trivial information about the
black hole interior and therefore do not constitute physical hair. We show that
this is also true for gravitational systems without horizon, for which both
injection and emission can be described classically. Moreover, we discuss and
clarify the role of infrared physics in purification.
