Polar Duality and Quasi-States: a Geometric Picture of Quantum Indeterminacy

The aim of this paper is to suggest a new interpretation of quantum indeterminacy using the notion of polar duality from convex geometry. Our approach does not involve the usual variances and covariances, whose use to describe quantum uncertainties has been questioned by Uffink and Hilgevoord. We introduce instead the geometric notion of "quasi-states" which are related in a way that will be explained to the notion of "quantum blob" we have introduced in previous work. Considering the symmetries of the quasi-states leads to the definition of the canonical group of a quasi-state, which allows to classify them.