A geometric proof of the Kochen-Specker no-go theorem

We give a short geometric proof of the Kochen-Specker no-go theorem for non-contextual hidden variables models. Note added to this version: I understand from Jan-Aake Larsson that the construction we give here actually contains the original Kochen-Specker construction as well as many others (Bell, Conway and Kochen, Schuette, perhaps also Peres).Comment: This paper appeared some years ago, before the author was aware of quant-ph. It is relevant to recent developments concerning Kochen-Specker theorem

Contextualism And Nonlocality In Quantum Mechanics

I describe the conceptual problems associated with the Kochen-Specker theorem including the presuppositions of the theorem and plausible interpretations of the conclusions motivated by the theorem. I describe an idealized quantum system which demonstrates both the Kochen-Specker theorem and the Bell argument for nonlocality. I present new findings about the mathematical structures which support a proof of the Kochen-Specker theorem

The generalized Kochen-Specker theorem

A proof of the generalized Kochen-Specker theorem in two dimensions due to Cabello and Nakamura is extended to all higher dimensions. A set of 18 states in four dimensions is used to give closely related proofs of the generalized Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference have been adde

MGP versus Kochen-Specker condition in hidden variables theories

Hidden variables theories for quantum mechanics are usually assumed to satisfy the KS condition. The Bell-Kochen-Specker theorem then shows that these theories are necessarily contextual. But the KS condition can be criticized from an operational viewpoint, which suggests that a weaker condition (MGP) should be adopted in place of it. This leads one to introduce a class of hidden parameters theories in which contextuality can, in principle, be avoided, since the proofs of the Bell-Kochen-Specker theorem break down. A simple model recently provided by the author for an objective interpretation of quantum mechanics can be looked at as a noncontextual hidden parameters theory, which shows that such theories actually exist.Comment: 10 pages, new updated footnotes and quotation

Alice and Bob get away with it: A playlet

Alice and Bob use Aravind's version of the Bell-Kochen-Specker theorem to fend off awkward questions about what exactly they were doing in Amsterdam last week

Kochen-Specker theorem studied with neutron interferometer

The Kochen-Specker theorem theoretically shows evidence of the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments by using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement in a single neutron system. Here entanglement is achieved not between different particles, but between degrees of freedom, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality of the Kochen-Specker theorem. The observed value of (2.291 +/- 0.008), which is above the threshold of 1, clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.Comment: 5 pages, 3 figure

Finite precision measurement nullifies the Kochen-Specker theorem

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 Kochen-Specker constructions does not obtain. Thus, in contrast to violation of the Bell inequalities, no quantum-over-classical advantage for information processing can be derived from the Kochen-Specker theorem alone.Comment: 7 pages, plain TeX; minor corrections, interpretation clarified, references update

Contextuality and the fundamental theorems of quantum mechanics

Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr and later realised more technically by Kochen and Specker. Isham and Butterfield put contextuality at the heart of their topos-based formalism and gave a reformulation of the Kochen-Specker theorem in the language of presheaves. Here, we broaden this perspective considerably (partly drawing on existing, but scattered results) and show that apart from the Kochen-Specker theorem, also Wigner's theorem, Gleason's theorem, and Bell's theorem relate fundamentally to contextuality. We provide reformulations of the theorems using the language of presheaves over contexts and give general versions valid for von Neumann algebras. This shows that a very substantial part of the structure of quantum theory is encoded by contextuality.Comment: v2: minor revisions, added definition of Bell presheaf, adjustment of Bell's theorem in contextual for