State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts

@misc{citeulike:1145668, 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.}, archivePrefix = {arXiv}, author = {Aerts, Diederik and Deses, Didier}, citeulike-article-id = {1145668}, eprint = {quant-ph/0404070}, keywords = {classicality, closure, closure-lattice, closure-space, closure-structures, connectedness, fca, lattice-of-closures, lattice-of-properties, logical-structures, non-classicality, property-lattice, separability, state-property-system, superselection, topological-space}, month = {Apr}, posted-at = {2007-03-07 14:05:18}, priority = {2}, title = {State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts}, url = {http://arxiv.org/abs/quant-ph/0404070}, year = {2004} }

TY - ELEC ID - citeulike:1145668 L3 - citeulike-article-id:1145668 N2 - 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. TI - State Property Systems and Closure Spaces: Extracting the Classical and Nonclassical Parts KW - classicality KW - closure KW - closure-lattice KW - closure-space KW - closure-structures KW - connectedness KW - fca KW - lattice-of-closures KW - lattice-of-properties KW - logical-structures KW - non-classicality KW - property-lattice KW - separability KW - state-property-system KW - superselection KW - topological-space AU - Aerts, Diederik AU - Deses, Didier PY - 2004/Apr/12/ UR - http://arxiv.org/abs/quant-ph/0404070 ER -