An epistemic interpretation of quantum probability via contextuality

TL;DR

This paper demonstrates that quantum probability can be interpreted epistemically using classical probability measures on contextual sets, explaining quantum non-Kolmogorovian structure through macroscopic and microscopic contexts.

Contribution

It introduces a framework using classical probability measures on contexts to interpret quantum probabilities epistemically, bridging classical and quantum probability structures.

Findings

Quantum probability can be epistemically interpreted with classical measures.

The framework explains the distinction between compatible and incompatible properties.

Classical conditional probabilities coexist with quantum conditional probabilities.

Abstract

According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the microscopic contexts (mu-contexts) underlying them, that one can interpret quantum probability as epistemic, despite its non-Kolmogorovian structure. To attain this result we introduce a predicate language L(x), a classical probability measure on it and a family of classical probability measures on sets of mu contexts, each element of the family corresponding to a (macroscopic) measurement procedure. By using only Kolmogorovian probability measures we can thus define mean conditional probabilities on the set of properties of any quantum system that admit an epistemic interpretation but are not bound to satisfy Kolmogorov's axioms. The generalized probability measures associated with states in QM can then be seen as special cases of these mean probabilities, which explains how they can be non-classical and provides them with an epistemic interpretation. Moreover, the distinction between compatible and incompatible properties is explained in a natural way, and purely theoretical classical conditional probabilities coexist with empirically testable quantum conditional probabilities.