A maximum value for the Kullback-Leibler divergence between quantum discrete distributions

This work presents an upper-bound for the maximum value that the Kullback-Leibler (KL) divergence from a given discrete probability distribution P can reach. In particular, the aim is to find a discrete distribution Q which maximizes the KL divergence from a given P under the assumption that P and Q have been generated by distributing a fixed discretized quantity. In addition, infinite divergences are avoided. The theoretical findings are used for proposing a notion of normalized KL divergence that is empirically shown to behave differently from already known measures.