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20 January 2021
 
  » arxiv » quant-ph/0008061

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Classical representations for quantum-like systems through an axiomatics for context dependence
Bob Coecke ;
Date 14 Aug 2000
Journal Helvetica Physica Acta 70, 442-461 (1997)
Subject Quantum Physics; Mathematical Physics | quant-ph math-ph math.MP
AbstractWe 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).
Source arXiv, quant-ph/0008061
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