Related papers: Contextuality with a Small Number of Observables
While non-contextual hidden-variable theories are proved to be impossible, contextual ones are possible. In a contextual hidden-variable theory, an observable is called a beable if the hidden-variable assigns its value in a given…
A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement…
There are contextual sets of multiple qubits whose commutation is parametrized thanks to the coset geometry $\mathcal{G}$ of a subgroup $H$ of the two-generator free group $G=\left\langle x,y\right\rangle$. One defines geometric…
Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and in this way derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations Hilbert spaces are naturally organised, by a…
Kochen-Specker (KS) vector systems are sets of vectors in R^3 with the property that it is impossible to assign 0s and 1s to the vectors in such a way that no two orthogonal vectors are assigned 0 and no three mutually orthogonal vectors…
We introduce a new framework for contextuality based on simplicial sets, combinatorial models of topological spaces that play a prominent role in modern homotopy theory. Our approach extends measurement scenarios to consist of spaces…
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…
The Local Friendliness argument is an extended Wigner's friend no-go theorem that provides strong constraints on the nature of reality -- stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we…
Magic sets of observables are minimal structures that capture quantum state-independent advantage for systems of $n\ge 2$ qubits and are, therefore, fundamental tools for investigating the interface between classical and quantum physics. A…
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…
Since the enlightening proofs of quantum contextuality first established by Kochen and Specker, and also by Bell, various simplified proofs have been constructed to exclude the non-contextual hidden variable theory of our nature at the…
It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual…
We show that if a finite point set $P\subseteq \mathbb{R}^2$ has the fewest congruence classes of triangles possible, up to a constant $M$, then at least one of the following holds. (1) There is a $\sigma>0$ and a line $l$ which contains…
A very simple illustration of the Bell-Kochen-Specker contradiction is presented using continuous observables in infinite dimensional Hilbert space. It is shown that the assumption of the \emph{existence} of putative values for position and…
We analyze the validity of Bell and Kochen-Specker theorems under local (or noncontextual) realism but avoiding an assumption of the existence of a joint probability distribution for incompatible observables. We formulate a realist model…
I will argue that the Peres-Mermin square does not necessarily rule out a value-definite (deterministic) noncontextual hidden variable model if the operators are not given a physical interpretation satisfying the following two requirements:…
Contextuality is a key distinguishing feature between classical and quantum physics. It expresses a fundamental obstruction to describing quantum theory using classical concepts. In turn, understood as a resource for quantum computation, it…
A proof of the Kochen-Specker theorem for a single two-level system is presented. It employs five eight-element positive operator-valued measures and a simple algebraic reasoning based on the geometry of the dodecahedron.
We present a general framework for contextuality tests in phase space using displacement operators. First, we derive a general condition that a single-mode displacement operator should fulfill in order to construct Peres-Mermin square and…
This paper studies how spatial thinking interacts with simplicity in [informal] proof, by analysing a set of example proofs mainly concerned with Ferrers diagrams (visual representations of partitions of integers, and comparing them to…