  Because the gravitational Hamiltonian is a pure boundary term on-shell,
asymptotic gravitational fields store information in a manner not possible in
local field theories. This fact has consequences for both perturbative and
non-perturbative quantum gravity. In perturbation theory about an
asymptotically flat collapsing black hole, the algebra generated by asymptotic
fields on future null infinity within any neighborhood of spacelike infinity
contains a complete set of observables. Assuming that the same algebra remains
complete at the non-perturbative quantum level, we argue that either 1) the
S-matrix is unitary or 2) the dynamics in the region near timelike, null, and
spacelike infinity is not described by perturbative quantum gravity about flat
space. We also consider perturbation theory about a collapsing asymptotically
anti-de Sitter (AdS) black hole, where we show that the algebra of boundary
observables within any neighborhood of any boundary Cauchy surface is similarly
complete. Whether or not this algebra continues to be complete
non-perturbatively, the assumption that the Hamiltonian remains a boundary term
implies that information available at the AdS boundary at any one time t_1
remains present at this boundary at any other time t_2.
