dorsal/arxiv
View SchemaClassical representations for quantum-like systems through an axiomatics for context dependence
| Authors | Bob Coecke |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0008061 |
| URL | https://arxiv.org/abs/quant-ph/0008061 |
| Journal | Helvetica Physica Acta 70, 442-461 (1997) |
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).
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"abstract": "We introduce a definition for a \u0027hidden measurement system\u0027, i.e., a physical\nentity for which there exist: (i) \u0027a set of non-contextual states of the entity\nunder study\u0027 and (ii) \u0027a set of states of the measurement context\u0027, and which\nare such that all uncertainties are due to a lack of knowledge on the actual\nstate of the measurement context. First we identify an explicit criterion that\nenables us to verify whether a given hidden measurement system is a\nrepresentation of a given couple $\\Si,{\\cal E}$ consisting of a set of states\n$\\Si$ and a set of measurements ${\\cal E}$ ($=$ measurement system). Then we\nprove for every measurement system that there exists at least one\nrepresentation as a hidden measurement system with $[0,1]$ as set of states of\nthe measurement context. Thus, we can apply this definition of a hidden\nmeasurement system to impose an axiomatics for context dependence. We show that\nin this way we always find classical representations (hidden measurement\nrepresentations) for general non-classical entities (e.g. quantum entities).",
"arxiv_id": "quant-ph/0008061",
"authors": [
"Bob Coecke"
],
"categories": [
"quant-ph",
"math-ph",
"math.MP"
],
"journal_ref": "Helvetica Physica Acta 70, 442-461 (1997)",
"title": "Classical representations for quantum-like systems through an axiomatics for context dependence",
"url": "https://arxiv.org/abs/quant-ph/0008061"
},
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