  We argue that if black hole entropy arises from a finite number of underlying
quantum states, then any particular such state can be identified from infinity.
The finite density of states implies a discrete energy spectrum, and, in
general, such spectra are non-degenerate except as determined by symmetries.
Therefore, knowledge of the precise energy, and of other commuting conserved
charges, determines the quantum state. In a gravitating theory, all conserved
charges including the energy are given by boundary terms that can be measured
at infinity. Thus, within any theory of quantum gravity, no information can be
lost in black holes with a finite number of states. However, identifying the
state of a black hole from infinity requires measurements with Planck scale
precision. Hence observers with insufficient resolution will experience
information loss.

High Energy Physics - Theory;General Relativity and Quantum Cosmology