On the notion of coexistence in quantum mechanics

TL;DR

This paper surveys the concept of coexistence in quantum mechanics, exploring formalizations, examples, and the relationship between joint measurability, noncommutativity, and measurement aspects.

Contribution

It provides a comprehensive review of formalizations of coexistence and examines the nuanced relationship between joint measurability and noncommuting observables.

Findings

Unsharpness enables joint measurement of noncommuting observables.

Noncoexistent observables can sometimes be measured together.

Reconsideration of the link between joint measurability and noncommutativity.

Abstract

The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of observables and of the statistical and individual aspects of quantum measurements.