  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.
