On the origin of nonclassicality in single systems

TL;DR

This paper explores the roots of nonclassical features in single systems within general probability theories, linking them to the non-simpliciality of the state space and discussing their implications for ontological models.

Contribution

It establishes a connection between various nonclassical features and the non-simpliciality of the state space in general probability theories, offering insights into their foundational origins.

Findings

Nonclassical features are linked to non-simpliciality of the state space.

Contextuality is an independent nonclassical feature.

An underlying simplex can serve as an ontological model.

Abstract

In the framework of certain general probability theories of single systems, we identify various nonclassical features such as incompatibility, multiple pure-state decomposability, measurement disturbance, no-cloning and the impossibility of certain universal operations, with the non-simpliciality of the state space. This is shown to naturally suggest an underlying simplex as an ontological model. Contextuality turns out to be an independent nonclassical feature, arising from the intransitivity of compatibility.