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26
Finite precision measurement nullifies the KochenSpecker theorem
, 1999
"... Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S 2, can be colored so that the contradiction with hidden variable theories provided by KochenSpecker constructions do ..."
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Cited by 32 (1 self)
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Only finite precision measurements are experimentally reasonable, and they cannot distinguish a dense subset from its closure. We show that the rational vectors, which are dense in S 2, can be colored so that the contradiction with hidden variable theories provided by KochenSpecker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantumoverclassical advantage for information processing can be derived from the KochenSpecker theorem alone.
Ensembles and Experiments in Classical and Quantum Physics
 Int. J. Mod. Phys. B
, 2003
"... A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical real ..."
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Cited by 8 (5 self)
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A philosophically consistent axiomatic approach to classical and quantum mechanics is given. The approach realizes a strong formal implementation of Bohr's correspondence principle. In all instances, classical and quantum concepts are fully parallel: the same general theory has a classical realization and a quantum realization.
Coloring the Rational Quantum Sphere and the KochenSpecker Theorem
"... We review and extend recent ndings of Godsil and Zaks [1], who published a constructive coloring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the sphere, exactly one ray is red, white and black. They also ..."
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Cited by 4 (0 self)
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We review and extend recent ndings of Godsil and Zaks [1], who published a constructive coloring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the sphere, exactly one ray is red, white and black. They also showed that any consistent coloring of the real sphere requires an additional color. We discuss some of the consequences for the KochenSpecker theorem [2].
Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem
 Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 35, 177194
, 2004
"... 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 th ..."
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Cited by 3 (1 self)
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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. 1. Gleason’s Theorem and Logical Compactness Kochen and Specker’s (1967) theorem (KS) puts a severe constraint on possible hiddenvariable interpretations of quantum mechanics. Often it is considered an improvement on a similar argument derived from Gleason (1957) theorem (see, for example, Held. 2000). This is true in the sense that KS provide an explicit construction of a finite set of rays on which no twovalued homomorphism exists. However, the fact that there is such a finite set follows from Gleason’s theorem using a simple logical compactness argument (Pitowsky 1998, a similar point is made in Bell 1996). The existence of finite sets of rays with other interesting features
Noncontextuality, finite precision measurement and the Kochen–Specker theorem
, 2003
"... Meyer originally raised the question of whether noncontextual hidden variable models can, despite the KochenSpecker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental ..."
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Cited by 2 (0 self)
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Meyer originally raised the question of whether noncontextual hidden variable models can, despite the KochenSpecker theorem, simulate the predictions of quantum mechanics to within any fixed finite experimental
On Generalized Probabilities: Correlation Polytopes for Automaton Logic and Generalized Urn Models, Extensions of Quantum Mechanics and Parameter Cheats
, 2001
"... Three extensions and reinterpretations of nonclassical probabilities are reviewed. ..."
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Three extensions and reinterpretations of nonclassical probabilities are reviewed.
On Coloring the Rational Quantum Sphere
, 2000
"... We discuss types of colorings of the rational quantum sphere similar to the one suggested recently by Meyer [1], in particular the consequences for the KochenSpecker theorem and for the correlation functions of entangled subsystems. ..."
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Cited by 1 (0 self)
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We discuss types of colorings of the rational quantum sphere similar to the one suggested recently by Meyer [1], in particular the consequences for the KochenSpecker theorem and for the correlation functions of entangled subsystems.
An obstruction based approach to the KochenSpecker theorem
, 1999
"... In [1] it was shown that the Kochen Specker theorem can be written in terms of the nonexistence of global elements of a certain varying set over the category W of boolean subalgebras of projection operators on some Hilbert space H. In this paper, we show how obstructions to the construction of such ..."
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In [1] it was shown that the Kochen Specker theorem can be written in terms of the nonexistence of global elements of a certain varying set over the category W of boolean subalgebras of projection operators on some Hilbert space H. In this paper, we show how obstructions to the construction of such global elements arise, and how this provides a new way of looking at proofs of the theorem.