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

TL;DR

This paper offers a novel geometric interpretation of quantum indeterminacy using polar duality and introduces the concept of quasi-states, providing a new framework that avoids traditional variance-based uncertainty measures.

Contribution

It introduces the notion of quasi-states and the concept of quantum blobs, offering a geometric perspective on quantum uncertainties distinct from traditional variance-based approaches.

Findings

Quasi-states are related to quantum blobs, providing a geometric interpretation.

The canonical group of a quasi-state classifies these states based on symmetries.

The approach avoids the use of variances and covariances in describing quantum indeterminacy.

Abstract

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.