Related papers: Generalised Kochen-Specker Theorem for Finite Non-…
A recent claim that finite precision in the design of real experiments ``nullifies'' the impact of the Kochen-Specker theorem, is shown to be unsupportable, because of the continuity of probabilities of measurement outcomes under slight…
The Kochen-Specker theorem asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which…
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…
It has recently been questioned whether the Kochen-Specker theorem is relevant to real experiments, which by necessity only have finite precision. We give an affirmative answer to this question by showing how to derive hidden-variable…
The failure of distributivity in quantum logic is motivated by the principle of quantum superposition. However, this principle can be encoded differently, i.e., in different logico-algebraic objects. As a result, the logic of experimental…
In the paper it is shown that the Kochen-Specker theorem follows from Burnside's theorem on noncommutative algebras. Accordingly, contextuality (as an impossibility of assigning binary values to projection operators independently of their…
A key ingredient of the Kochen-Specker theorem is the so-called functional composition principle, which asserts that hidden states must ascribe values to observables in a way that is consistent with all functional relations between them.…
We present an experimental scheme for the implementation of arbitrary generalized measurements, represented by positive-operator valued measures, on the polarization of single photons, using linear optical devices. Further, we…
We show that a reduced form of the structural requirements for deterministic hidden variables used in Bell-Kochen-Specker theorems is already sufficient for the no-go results. Those requirements are captured by the following principle: an…
Within the framework of quantum contextuality, we discuss the ideas of extracontextuality and extravalence, that allow one to relate Kochen-Specker's and Gleason's theorems. We emphasize that whereas Kochen-Specker's is essentially a no-go…
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…
We develop a general, non-probabilistic model of prediction which is suitable for assessing the (un)predictability of individual physical events. We use this model to provide, for the first time, a rigorous proof of the unpredictability of…
The Kochen-Specker theorem shows that it is impossible to assign sharp values to all dynamical variables in quantum mechanics in such a way that the algebraic relations among the values of dynamical variables whose self-adjoint operators…
When it isn't possible to tell two distinct experimental procedures apart purely from their input/output statistics, then it seems a plausible hypothesis that the two procedures must be physically identical. We call such a hypothesis…
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…
Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists…
Recently, quantum contextuality has been proved to be the source of quantum computation's power. That, together with multiple recent contextual experiments, prompts improving the methods of generation of contextual sets and finding their…
It is shown that the quantum theory can be formulated on homogeneous spaces of generalized coherent states in a manner that accounts for interference, entanglement, and the linearity of dynamics without using the superposition principle.…
A Kochen-Specker (KS) set is a specific set of projectors and measurement contexts that prove the Bell-Kochen-Specker contextuality theorem. The simplest known KS sets in Hilbert space dimensions $d=3,4,5,6,8$ are reproduced, and several…
It is proven that any hidden variable theory of the type proposed by Meyer [Phys. Rev. Lett. {\bf 83}, 3751 (1999)], Kent [{\em ibid.} {\bf 83}, 3755 (1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A {\bf 456}, 2101 (2000)] leads…