  We explore the relationship between the quantum state of a compact matter
source and of its asymptotic graviton field. For a matter source in an energy
eigenstate, the graviton state is determined at leading order by the energy
eigenvalue. Insofar as there are no accidental energy degeneracies there is a
one to one map between graviton states on the boundary of spacetime and the
matter source states. A typical semiclassical matter source results in an
entangled asymptotic graviton state. We exhibit a purely quantum gravitational
effect which causes the subleading asymptotic behavior of the graviton state to
depend on the internal structure of the source. These observations establish
the existence of ubiquitous quantum hair due to gravitational effects.
