Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem

Details Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem

2003-07-19

arxiv.org/abs/quant-ph/0307139v1

Physics

Quantum Physics

14 pages, 6 figures, read at the Robert Clifton memorial conference

Scientific paper

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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