Related papers: Gadget structures in proofs of the Kochen-Specker …
We give a constructive and exhaustive definition of Kochen-Specker (KS) vectors in a Hilbert space of any dimension as well as of all the remaining vectors of the space. KS vectors are elements of any set of orthonormal states, i.e.,…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
A simple three rules supplemented by five steps scheme is proposed to produce Kochen-Specker (KS) sets with 30 rank-2 projectors that occur twice each. The KS sets provide state-independent proof of KS theorem based on a system of three…
The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…
In the history of quantum physics several no-go theorems have been proved, and many of them have played a central role in the development of the theory, such as Bell's or the Kochen-Specker theorem. A recent paper by F. Laudisa has raised…
The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…
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…
We introduce two generalizations of Kochen-Specker (KS) sets: projective KS sets and generalized KS sets. We then use projective KS sets to characterize all graphs for which the chromatic number is strictly larger than the quantum chromatic…
The {\em distinguishing number} of a group $G$ acting faithfully on a set $V$ is the least number of colors needed to color the elements of $V$ so that no non-identity element of the group preserves the coloring. The {\em distinguishing…
We derive inequalities for $n$ spin-1/2 systems under the assumption that the hidden-variable theoretical joint probability distribution for any pair of commuting observables is equal to the quantum mechanical one. Fine showed that this…
We introduce an original model of quantum phenomena, a model that provides a picture of a "deep structure", an "underlying pattern" of quantum dynamics. We propose that the source of a particle and all of that particle's possible detectors…
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…
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…
A recent claim by Meyer, Kent and Clifton (MKC), that their models ``nullify'' the Kochen-Specker theorem, has attracted much comment. In this paper we present a new counter-argument, based on the fact that a classical measurement reveals,…
It was presented by Cabello and Nakamura [A. Cabello, Phys. Rev. Lett. 90, 190401 (2003)], that the Kochen-Specker theorem applies to two dimensions if one uses Positive Operator-Valued Measures. We show that contextuality in their models…
We construct a new graph on 120 vertices whose quantum and classical independence numbers are different. At the same time, we construct an infinite family of graphs whose quantum chromatic numbers are smaller than the classical chromatic…
The concept of individuality in quantum mechanics shows radical differences from the one used in classical physics. In particular, it is not possible to consider the fundamental particles described by quantum theory as individual…
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 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…
Algorithms for finding arbitrary sets of Kochen-Specker (KS) qunits (n-level systems) as well as all the remaining vectors in a space of an arbitrary dimension are presented. The algorithms are based on linear MMP diagrams which generate…