Related papers: The relation between the Kochen-Specker theorem an…
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…
The purpose of this note is to complete the interesting review on quantum contextuality [1] that appeared recently. In particular we will introduce and discuss the ideas of extracontextuality and extravalence, that allow one to relate…
Certain concrete "ontological models" for quantum mechanics (models in which measurement outcomes are deterministic and quantum states are equivalent to classical probability distributions over some space of `hidden variables') are…
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…
According to Pavi\v{c}i{\'c}, Kochen and Specker's 117-observable set is not a ``Kochen-Specker set''. By the same reason, in arXiv:2502.13787, Pavi\v{c}i{\'c} claims that 10 statements in our paper ``Optimal conversion of Kochen-Specker…
A recent proposal to experimentally test quantum mechanics against noncontextual hidden-variable theories [Phys. Rev. Lett. 80, 1797 (1998)] is shown to be related with the smallest proof of the Kochen-Specker theorem currently known [Phys.…
We present a toy theory that is based on a simple principle: the number of questions about the physical state of a system that are answered must always be equal to the number that are unanswered in a state of maximal knowledge. A wide…
In an empirical logic, an experimentally verifiable proposition P relating to a quantum system is assigned the value of either true of false if the system is in the pure state that belongs or, respectively, does not belong to the Hilbert…
The Kochen-Specker theorem states that a 3-dimensional complex Euclidean space admits a finite configuration of projective lines such that the corresponding quantum observables (the orthogonal projectors) cannot be assigned with 0 and 1…
Contextuality is one of the fundamental deviations of quantum mechanics from classical physics. The Kochen-Specker (KS) theorem shows that non-contextual classical physics with hidden variables is inconsistent with the predictions of…
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…
It is shown that in two-state quantum theory, a generic quantum state can be described by a non-computable real number. In terms of this, the criterion for measurement outcome is simply and deterministically defined. This demonstration is…
Fully revealing the mathmatical structure of quantum contextuality is a significant task, while some known contextuality theories are only applicable for rank-1 projectors. That is because they adopt the observable-based definitions. This…
Two notions of nonclassicality that have been investigated intensively are: (i) negativity, that is, the need to posit negative values when representing quantum states by quasiprobability distributions such as the Wigner representation, and…
Proofs of Bell-Kochen-Specker contextuality demonstrate that there exists sets of projectors that cannot each be assigned either 0 or 1 such that each basis formed from them contains exactly one 1-assigned projector. Instead, at least some…
We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient…
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…
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…
Several arguments demonstrate the incompatibility between Quantum Mechanics and classical Physics. Bell's inequalities and Greenberger-Horne-Zeilinger (GHZ) arguments apply to specific non-classical states. The Kochen-Specker (KS) one,…
Every measurement determines a single value as its outcome, and yet quantum mechanics predicts it only probabilistically. The Kochen-Specker theorem and Bell's inequality are often considered to reject a realist view but favor a skeptical…