Imprecise probability for non-commuting observables

Abstract

It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (additive) probability model. I show that the joint distribution of any non-commuting pair of variables can be quantified via upper and lower probabilities, i.e. the joint probability is described by an interval instead of a number (imprecise probability). I propose transparent axioms from which the upper and lower probability operators follow. They depend only on the non-commuting observables and revert to the usual expression for the commuting case.

4 pages, single-column, revtex + supplementary material

References in corpus (3)

• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Non-equilibrium quantum fluctuations of work
• Quantum Mechanics and imprecise probability

Cited by in corpus (6)

• Perspective: Quantum Thermodynamics
• Conditions tighter than noncommutation needed for nonclassicality
• Properties and Applications of the Kirkwood-Dirac Distribution
• Characterizing the geometry of the Kirkwood-Dirac positive states
• Excluding joint probabilities from quantum theory
• Quantum non-locality co-exists with locality