dorsal/arxiv
View SchemaState property systems and orthogonality
| Authors | Dirk Aerts, Didier Deses |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0211095 |
| URL | https://arxiv.org/abs/quant-ph/0211095 |
| DOI | 10.1007/s10773-005-7069-4 |
| Journal | International Journal of Theoretical Physics 44, pp. 919-929 (2005) |
Abstract
The structure of a state property system was introduced to formalize in a complete way the operational content of the Geneva-Brussels approach to the foundations of quantum mechanics, and the category of state property systems was proven to be equivalence to the category of closure spaces. The first axioms of standard quantum axiomatics (state determination and atomisticity) have been shown to be equivalent to the $T_0$ and $T_1$ axioms of closure spaces, and classical properties to correspond to clopen sets, leading to a decomposition theorem into classical and purely nonclassical components for a general state property system. The concept of orthogonality, very important for quantum axiomatics, had however not yet been introduced within the formal scheme of the state property system. In this paper we introduce orthogonality in a operational way, and define ortho state property systems. Birkhoff's well known biorthogonal construction gives rise to an orthoclosure and we study the relation between this orthoclosure and the operational orthogonality that we introduced.
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"abstract": "The structure of a state property system was introduced to formalize in a\ncomplete way the operational content of the Geneva-Brussels approach to the\nfoundations of quantum mechanics, and the category of state property systems\nwas proven to be equivalence to the category of closure spaces. The first\naxioms of standard quantum axiomatics (state determination and atomisticity)\nhave been shown to be equivalent to the $T_0$ and $T_1$ axioms of closure\nspaces, and classical properties to correspond to clopen sets, leading to a\ndecomposition theorem into classical and purely nonclassical components for a\ngeneral state property system. The concept of orthogonality, very important for\nquantum axiomatics, had however not yet been introduced within the formal\nscheme of the state property system. In this paper we introduce orthogonality\nin a operational way, and define ortho state property systems. Birkhoff\u0027s well\nknown biorthogonal construction gives rise to an orthoclosure and we study the\nrelation between this orthoclosure and the operational orthogonality that we\nintroduced.",
"arxiv_id": "quant-ph/0211095",
"authors": [
"Dirk Aerts",
"Didier Deses"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s10773-005-7069-4",
"journal_ref": "International Journal of Theoretical Physics 44, pp. 919-929\n (2005)",
"title": "State property systems and orthogonality",
"url": "https://arxiv.org/abs/quant-ph/0211095"
},
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