State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts
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.
Cite
@article{arxiv.quant-ph/0404070,
title = {State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts},
author = {Diederik Aerts and Didier Deses},
journal= {arXiv preprint arXiv:quant-ph/0404070},
year = {2010}
}
Comments
15 pages, 2 figures, Published in Probing the Structure of Quantum Mechanics: Nonlinearity, Nonlocality, Probability and Axiomatics, eds. Aerts, D, Czachor, M. and Durt, T, World Scientific, Singapore