Hierarchical axioms for quantum mechanics

TL;DR

This paper establishes a hierarchy of five nonclassical features that distinguish quantum mechanics from classical theories, providing a structured framework within generalized probability theories to understand quantum nonclassicality.

Contribution

It introduces a hierarchical framework of five nonclassical features in quantum mechanics, clarifying their logical independence and layered structure within generalized probability theories.

Findings

Identifies five nonclassical features forming a hierarchy in QM

Illustrates each layer with toy GPTs to show their role

Clarifies the logical independence of nonclassical axioms

Abstract

The origin of nonclassicality in quantum mechanics (QM) has been investigated recently by a number of authors with a view to identifying axioms that would single out quantum mechanics as a special theory within a broader framework such as convex operational theories. In these studies, the axioms tend to be logically independent in the sense that no specific ordering of the axioms is implied. Here, we identify a hierarchy of five nonclassical features that separate QM from a classical theory: (Q1) Incompatibility and indeterminism; (Q2) Contextuality; (Q3) Entanglement; (Q4) Nonlocality and (Q5) Indistinguishability of identical particles. Such a hierarchy isn't obvious when viewed from within the quantum mechanical framework, but, from the perspective of generalized probability theories (GPTs), the later axioms can be regarded as further structure introduced on top of earlier axioms. Relevant toy GPTs are introduced at each layer when useful to illustrate the action of the nonclassical features associated with the particular layer.