On the notion of coexistence in quantum mechanics

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.

References in corpus (6)

• Heisenberg's Uncertainty Principle
• Coexistence of qubit effects
• Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
• A note on the measurement of phase space observables with an eight-port homodyne detector
• Position and momentum tomography
• Joint measurement of two unsharp observables of a qubit

Cited by in corpus (6)

• Coexistence does not imply joint measurability
• Quantum information as a non-Kolmogorovian generalization of Shannon's theory
• On coexistence and joint measurability of rank-1 quantum observables
• On the lattice structure of probability spaces in quantum mechanics
• Quantal effects and MaxEnt
• Generalized probabilities in statistical theories