  Based on an intuitive generalization of the Leibniz principle of `the
identity of indiscernibles', we introduce a novel ontological notion of
classicality, called bounded ontological distinctness. Formulated as a
principle, bounded ontological distinctness equates the distinguishability of a
set of operational physical entities to the distinctness of their ontological
counterparts. Employing three instances of two-dimensional quantum
preparations, we demonstrate the violation of bounded ontological distinctness
or excess ontological distinctness of quantum preparations, without invoking
any additional assumptions. Moreover, our methodology enables the inference of
tight lower bounds on the extent of excess ontological distinctness of quantum
preparations. Similarly, we demonstrate excess ontological distinctness of
quantum transformations, using three two-dimensional unitary transformations.
However, to demonstrate excess ontological distinctness of quantum
measurements, an additional assumption such as outcome determinism or bounded
ontological distinctness of preparations is required. Moreover, we show that
quantum violations of other well-known ontological principles implicate quantum
excess ontological distinctness. Finally, to showcase the operational vitality
of excess ontological distinctness, we introduce two distinct classes of
communication tasks powered by excess ontological distinctness.
