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arXiv · 1411.4319

Imprecise probability for non-commuting observables

A. E. Allahverdyan
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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.

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A. E. Allahverdyan. 2014-11-16. Imprecise probability for non-commuting observables. https://doi.org/10.1088/1367-2630%2F17%2F8%2F085005

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