  This work presents an upper-bound to value that the Kullback-Leibler (KL)
divergence can reach for a class of probability distributions called quantum
distributions (QD). The aim is to find a distribution $U$ which maximizes the
KL divergence from a given distribution $P$ under the assumption that $P$ and
$U$ have been generated by distributing a given discrete quantity, a quantum.
Quantum distributions naturally represent a wide range of probability
distributions that are used in practical applications. Moreover, such a class
of distributions can be obtained as an approximation of any probability
distribution. The retrieving of an upper-bound for the entropic divergence is
here shown to be possible under the condition that the compared distributions
are quantum distributions over the same quantum value, thus they become
comparable. Thus, entropic divergence acquires a more powerful meaning when it
is applied to comparable distributions. This aspect should be taken into
account in future developments of divergences. The theoretical findings are
used for proposing a notion of normalized KL divergence that is empirically
shown to behave differently from already known measures.
