  The conservation of information of evaporating black holes is a very natural
consequence of unitarity which is the fundamental symmetry of quantum
mechanics. In order to study the conservation of information, we need to
understand the nature of the entanglement entropy. The entropy of Hawking
radiation is approximately equal to the maximum of entanglement entropy if a
black hole is in a state before the Page time, i.e., when the entropy of
Hawking radiation is smaller than the entropy of the black hole. However, if
there exists a process generating smaller entanglements rather than maximal
entanglements, the entropy of Hawking radiation will become smaller than the
maximum of the entanglement entropy before the Page time. If this process
accumulates, even though the probability is small, the emitted radiation can
eventually be distinguished from the exactly thermal state. In this paper, we
provide several interpretations of this phenomenon: (1) information of the
collapsed matter is emitted before the Page time, (2) there exists a firewall
or a non-local effect before the Page time, or (3) the statistical entropy is
greater than the areal entropy; a monster is formed. Our conclusion will help
resolve the information loss paradox by providing groundwork for further
research.
