  The process of gravitational collapse excites the fields propagating in the
background geometry and gives rise to thermal radiation. We demonstrate by
explicit calculations that the density matrix corresponding to such radiation
actually describes a pure state. While Hawking's leading order density matrix
contains only the diagonal terms, we calculate the off-diagonal correlation
terms. These correlations start very small, but then grow in time. The
cumulative effect is that the correlations become comparable to the leading
order terms and significantly modify the density matrix. While the trace of the
Hawking's density matrix squared diverges from unity during the evolution, the
trace of the total density matrix squared remains unity at all times and all
frequencies. This implies that the process of radiation from a collapsing
object is unitary.
