  Empirical falsifiability of the predictions of physical theories is the
cornerstone of the scientific method. Physical theories attribute empirically
falsifiable operational properties to sets of physical preparations. A theory
is said to be empirically complete if such properties allow for a not
fine-tuned realist explanation, as properties of underlying probability
distributions over states of reality. Such theories satisfy a family of
equalities among fundamental operational properties, characterized exclusively
by the number of preparations. Quantum preparations deviate from these
equalities, and the maximal quantum deviation increases with the number of
preparations. These deviations not only signify the incompleteness of the
operational quantum formalism, but they simultaneously imply quantum over
classical advantage in suitably constrained one-way communication tasks,
highlighting the delicate interplay between the two.
