Related papers: Kochen-Specker Theorem: Two Geometric Proofs
We present an elementary proof of a reduced version of Gleason's theorem and the Kochen-Specker theorem to provide a novel perspective on the relation between both theorems. The proof is based on a set of linear equations for the values of…
Mermin's simple "pentagram" proof of the Kochen-Specker theorem is examined from various perspectives. We emphasise the many mathematical structures intimately related to Kochen-Specker proofs, ranging through functional analysis, sheaf…
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…
A number of new proofs of the Kochen-Specker theorem are given based on the observables of the three-qubit Pauli group. Each proof is presented in the form of a diagram from which it is obvious by inspection. Each of our observable-based…
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…
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…
A generalized Kochen-Specker theorem is proved. It is shown that there exist sets of $n$ projection operators, representing $n$ yes-no questions about a quantum system, such that none of the $2^n$ possible answers is compatible with sum…
The Kochen-Specker theorem is a basic and fundamental 50 year old non-existence result affecting the foundations of quantum mechanix, strongly implying the lack of any meaningful notion of "quantum realism", and typically leading to…
We discuss two approaches to producing generalized parity proofs of the Kochen-Specker theorem. Such proofs use contexts of observables whose product is $I$ or $-I$; we call them constraints. In the first approach, one starts with a fixed…
The Kochen-Specker theorem has been discussed intensely ever since its original proof in 1967. It is one of the central no-go theorems of quantum theory, showing the non-existence of a certain kind of hidden states models. In this paper, we…
Coxeter pointed out that a number of polytopes can be projected orthogonally into two dimensions in such a way that their vertices lie on a number of concentric regular triacontagons (or 30-gons). Among them are the 600-cell and 120-cell in…
I review the two theorems referred to in the title, and then suggest that it would be interesting to know how much of Hilbert space one can use without forcing the proof of these theorems. It would also be interesting to know what parts of…
The Kochen-Specker theorem is a fundamental result in quantum foundations that has spawned massive interest since its inception. We show that within every Kochen-Specker graph, there exist interesting subgraphs which we term $01$-gadgets,…
The Kochen-Specker theorem is one of the fundamental no-go theorems in quantum theory. It has far-reaching consequences for all attempts trying to give an interpretation of the quantum formalism. In this work, we examine the hypotheses…
We present a number of observables-based proofs of the Kochen-Specker (KS) theorem based on the N-qubit Pauli group for N >= 4, thus adding to the proofs that have been presented earlier for the two- and three-qubit groups. These proofs…
We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…
The Kochen-Specker Theorem is widely interpreted to imply that non-contextual hidden variable theories that agree with the predictions of Copenhagen quantum mechanics are impossible. The import of the theorem for a novel observer…
A Kochen-Specker contradiction is produced with 36 vectors in a real 8-dimensional Hilbert space. These vectors can be combined into 30 distinct projection operators (14 of rank 2, and 16 of rank 1). A state-specific variant of this…
In the paper it is argued that the Kochen-Specker theorem necessitates a conclusion that for a quantum system it is possible to find a set of projection operators which is not truth-value bivalent; that is, a bivalent truth-value assignment…
The Kochen-Specker (KS) theorem is a cornerstone result in quantum foundations, establishing that quantum correlations in Hilbert spaces of dimension $d \geq 3$ cannot be explained by (consistent) hidden variable theories that assign a…