CLASSICAL REPRESENTATIONS FOR QUANTUM-LIKE SYSTEMS THROUGH AN AXIOMATICS FOR CONTEXT DEPENDENCE

We introduce a definition for a 'hidden measurement system', i.e., a p hysical entity for which there exist: (i) 'a set of non-contextual sta tes of the entity under study' and (ii) 'a set of states of the measur ement context', and which are such that all uncertainties are due to a lack of knowledge on the actual state of the measurement; context. Fi rst we identify an explicit criterion that enables us to verify whethe r a given hidden measurement system is a representation of a given cou ple Sigma, E consisting of a set of states Sigma and a set of measurem ents E (= measurement system). Then we prove for every measurement sys tem that there exists at least one representation as a hidden measurem ent system with [0, 1] as set of states of the measurement context. Th us, we can apply this definition of a hidden measurement system to imp ose an axiomatics for context dependence. We show that in this way we always find classical representations (hidden measurement representati ons) for general non-classical entities (e.g, quantum entities).