dorsal/arxiv
View SchemaGeneralizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem
| Authors | Ehud Hrushovski, Itamar Pitowsky |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307139 |
| URL | https://arxiv.org/abs/quant-ph/0307139 |
Abstract
Kochen and Specker's theorem can be seen as a consequence of Gleason's theorem and logical compactness. Similar compactness arguments lead to stronger results about finite sets of rays in Hilbert space, which we also prove by a direct construction. Finally, we demonstrate that Gleason's theorem itself has a constructive proof, based on a generic, finite, effectively generated set of rays, on which every quantum state can be approximated.
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"abstract": "Kochen and Specker\u0027s theorem can be seen as a consequence of Gleason\u0027s\ntheorem and logical compactness. Similar compactness arguments lead to stronger\nresults about finite sets of rays in Hilbert space, which we also prove by a\ndirect construction. Finally, we demonstrate that Gleason\u0027s theorem itself has\na constructive proof, based on a generic, finite, effectively generated set of\nrays, on which every quantum state can be approximated.",
"arxiv_id": "quant-ph/0307139",
"authors": [
"Ehud Hrushovski",
"Itamar Pitowsky"
],
"categories": [
"quant-ph"
],
"title": "Generalizations of Kochen and Specker\u0027s Theorem and the Effectiveness of Gleason\u0027s Theorem",
"url": "https://arxiv.org/abs/quant-ph/0307139"
},
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