To what extent is quantum ambiguity ambiguous?

Abstract

A natural question arises in the framework of the unsharp approach to QT: to what extent is “sharp/unsharp” an unsharp, ambiguous distinction? So far, we have generally called sharp any quantum effect (or property) that satisfies the noncontradiction principle. However, different definitions of “sharp effect” can be proposed. One can distinguish two basic kinds of characterizations (Cattaneo, Dalla Chiara and Giuntini, 1999): (i) purely algebraic definitions, that only refer to the algebraic structure of the quantum effects; and (ii) probabilistic definitions, that also refer to the relationships between effects and states.