  In semiclassical gravity, the final state of black-hole evaporation cannot be
described by a pure state. Nevertheless, we point out that the system can be
described by a generalized pure state, which is not defined on a 3-dimensional
hypersurface but on the 4-dimensional spacetime describing the whole Universe
at all times. Unlike the conventional quantum state, such a generalized state
treats time on an equal footing with space, which makes it well suited for
systems that are both quantum and relativistic. In particular, such a
generalized state contains a novel type of information encoded in the
correlations between future and past, which avoids the black-hole information
paradox.
