  According to quantum mechanics, the informational content of isolated systems
does not change in time. However, subadditivity of entropy seems to describe an
excess of information when we look at single parts of a composite systems and
their correlations. Moreover, the balance between the entropic contributions
coming from the various parts is not conserved under unitary transformations.
Reasoning on the basic concept of quantum mechanics, we find that in such a
picture an important term has been overlooked: the intrinsic quantum
information encoded in the coherence of pure states. To fill this gap we are
led to define a quantity, that we call coherent entropy, which is necessary to
account for the "missing" information and for re-establishing its conservation.
Interestingly, the coherent entropy is found to be equal to the information
conveyed in the future by quantum states. The perspective outlined in this
paper may be of some inspiration in several fields, from foundations of quantum
mechanics to black-hole physics.
