  We study how the black hole complementarity principle can emerge from quantum
gravitational dynamics within a local semiclassical approximation. Further
developing and then simplifying a microstate model based on the fragmentation
instability of a near-extremal black hole, we find that the key to the
replication (but not cloning) of infalling information is the decoupling of
various degrees of freedom. The infalling matter decouples from the interior
retaining a residual time-dependent quantum state in the hair which encodes the
initial state of the matter non-isometrically. The non-linear ringdown of the
interior after energy absorption and decoupling also encodes the initial state,
and transfers the information to Hawking radiation. During the Hawking
evaporation process, the fragmented throats decouple from each other and the
hair decouples from the throats. We find that the hair mirrors infalling
information after the decoupling time which scales with the logarithm of the
entropy (at the time of infall) when the average mass per fragmented throat (a
proxy for the temperature) is held fixed. The decoding protocol for the
mirrored information does not require knowledge of the interior, and only
limited information from the Hawking radiation, as can be argued to be
necessitated by the complementarity principle. We discuss the scope of the
model to illuminate various aspects of information processing in a black hole.

High Energy Physics - Theory;Strongly Correlated Electrons;General Relativity and Quantum Cosmology;Quantum Physics