  We assess the extent of similarity between pairs of probability distributions
that arise naturally in quantum optics. We employ the Wasserstein distance, the
Kullback-Leibler divergence and the Bhattacharyya distance to compare different
states of light. We investigate the effectiveness of these quantifiers in
identifying nonclassical effects such as wave packet revival phenomena and
sudden changes in entanglement in generic bipartite systems. The calculations
are carried out on relevant optical tomograms, circumventing state
reconstruction.
