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

Hrushovski, Ehud; Pitowsky, Itamar

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

Authors

Description

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