Characterization of strong preparational uncertainty by superposition

Derive an operational formulation of strong preparational uncertainty entirely in terms of superposition states, without relying on the additional outcome-sharpness assumptions used for the corresponding formulations of existence and weak preparational uncertainty.

Background

The paper establishes equivalences between superposition and the existence or weak form of preparational uncertainty under outcome sharpness of maximally distinguishing and extremal measurements. It explicitly notes that an analogous characterization of strong uncertainty has not been obtained without such additional assumptions. Strong uncertainty is especially significant because, among the polygonal theories considered, it distinguishes real qubit quantum theory in the continuous limit.