Classical representations for quantum-like systems through an axiomatics for context dependence

TL;DR

This paper introduces a formal framework for representing quantum-like systems using classical models based on hidden measurement systems, emphasizing the role of context dependence in measurement uncertainties.

Contribution

It defines a criterion for representing measurement systems as hidden measurement systems and proves that all such systems can be classically represented with a standard measurement context set.

Findings

Existence of classical hidden measurement representations for quantum entities

A criterion to verify hidden measurement system representations

Application of axioms to impose context dependence in measurement models

Abstract

We introduce a definition for a 'hidden measurement system', i.e., a physical entity for which there exist: (i) 'a set of non-contextual states of the entity under study' and (ii) 'a set of states of the measurement context', and which are such that all uncertainties are due to a lack of knowledge on the actual state of the measurement context. First we identify an explicit criterion that enables us to verify whether a given hidden measurement system is a representation of a given couple $\Si,{\cal E}$ consisting of a set of states $\Si$ and a set of measurements ${\cal E}$ ($=$ measurement system). Then we prove for every measurement system that there exists at least one representation as a hidden measurement system with $[0,1]$ as set of states of the measurement context. Thus, we can apply this definition of a hidden measurement system to impose an axiomatics for context dependence. We show that in this way we always find classical representations (hidden measurement representations) for general non-classical entities (e.g. quantum entities).