. . . if the material entering the black hole were a pure

quantum state, the transformation of that state into the mixed state of Hawking radiation would destroy information about the original quantum state. This violates

Liouville's theorem and presents a

physical paradox.[

*citation needed*]

More precisely, if there is an

entangled pure state, and one part of the entangled system is thrown into the black hole while keeping the other part outside, the result is a mixed state after the

partial trace is taken into the interior of the black hole. But since everything within the interior of the black hole will hit the

singularity within a finite time, the part which is traced over partially might disappear completely from the physical system.[

*citation needed*]