  We show that for every qubit of quantum information, there is a well-defined
notion of "the amount of energy that carries it", because it is a conserved
quantity. This generalizes to larger systems and any conserved quantites: the
eigenvalue spectrum of conserved charges has to be preserved while transferring
quantum information. It is possible to "apparently" violate these conservations
by losing a small fraction of information, but that must invoke a specific
process which requires a large scale coherence. We discuss its implication
regarding the black hole information paradox.
