dorsal/arxiv
View SchemaState Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts
| Authors | Diederik Aerts, Didier Deses |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0404070 |
| URL | https://arxiv.org/abs/quant-ph/0404070 |
| Journal | In D. Aerts, M. Czachor and T. Durt (Eds.), Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics (pp. 130-148). Singapore: World Scientific, 2002. |
Abstract
We introduce classical properties using the concept of super selection rule, i.e. two properties are separated by a superselection rule iff there do not exist 'superposition states' related to these two properties. Then we show that the classical properties of a state property system correspond exactly to the clopen subsets of the corresponding closure space. Thus connected closure spaces correspond precisely to state property systems for which the elements 0 and I are the only classical properties, the so called pure nonclassical state property systems. The main result is a decomposition theorem, which allows us to split a state property system into a number of 'pure nonclassical state property systems' and a 'totally classical state property system'. This decomposition theorem for a state property system is the translation of a decomposition theorem for the corresponding closure space into its connected components.
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"abstract": "We introduce classical properties using the concept of super selection rule,\ni.e. two properties are separated by a superselection rule iff there do not\nexist \u0027superposition states\u0027 related to these two properties. Then we show that\nthe classical properties of a state property system correspond exactly to the\nclopen subsets of the corresponding closure space. Thus connected closure\nspaces correspond precisely to state property systems for which the elements 0\nand I are the only classical properties, the so called pure nonclassical state\nproperty systems. The main result is a decomposition theorem, which allows us\nto split a state property system into a number of \u0027pure nonclassical state\nproperty systems\u0027 and a \u0027totally classical state property system\u0027. This\ndecomposition theorem for a state property system is the translation of a\ndecomposition theorem for the corresponding closure space into its connected\ncomponents.",
"arxiv_id": "quant-ph/0404070",
"authors": [
"Diederik Aerts",
"Didier Deses"
],
"categories": [
"quant-ph"
],
"journal_ref": "In D. Aerts, M. Czachor and T. Durt (Eds.), Probing the Structure\n of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics\n (pp. 130-148). Singapore: World Scientific, 2002.",
"title": "State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts",
"url": "https://arxiv.org/abs/quant-ph/0404070"
},
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