Related papers: The Minimum Complexity of Kochen-Specker Sets Does…
Recently, handling of contextual sets, in particular Kochen-Specker (KS) sets, in higher dimensions has been given an increasing attention, both theoretically and experimentally. However, methods of their generation are diverse, not…
In Phys. Rev. Lett. 135, 190203 (2025) a discovery of the simplest 3D contextual set with 33 vertices, 50 bases, and 14 complete bases is claimed. In this paper, we show that it was previously generated in Quantum 7, 953 (2023) and analyze…
The Kochen-Specker (KS) theorem is a central result in quantum theory and has applications in quantum information. Its proof requires several yes-no tests that can be grouped in contexts or subsets of jointly measurable tests. Arguably, the…
Development of quantum computation and communication, recently shown to be supported by contextuality, arguably asks for a requisite supply of contextual sets. While that has been achieved in even dimensional spaces, in odd dimensional…
Kochen-Specker (KS) sets are fundamental in physics. Every time nature produces bipartite correlations attaining the nonsignaling limit, or two parties always win a nonlocal game impossible to always win classically, is because the parties…
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…
Kochen-Specker (KS) theorem denies the possibility for the noncontextual hidden variable theories to reproduce the predictions of quantum mechanics. A set of projection operators (projectors) and bases used to show the impossibility of…
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.,…
The challenge of determining bounds for the minimal number of vectors in a three-dimensional Kochen-Specker (KS) set has captivated the quantum foundations community for decades. This paper establishes a weak lower bound of 10 vectors,…
Recent results show that Kochen-Specker (KS) sets of observables are fundamental to quantum information, computation, and foundations beyond previous expectations. Among KS sets, those that are unique up to unitary transformations (i.e.,…
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…
We show that all possible 388 4-dim Kochen-Specker (KS) (vector) sets (of yes-no questions) with 18 through 23 vectors and 844 sets with 24 vectors all with component values from \{-1,0,1\} can be obtained by stripping vectors off a single…
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…
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics cannot be reconciled with classical models that are noncontextual for ideal measurements. The first explicit…
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…
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 present a systematic, constructive analysis of Kochen-Specker contextuality, emphasizing the foundational importance of complete orthogonal bases (contexts). First, in three dimensions, we generate a complete inventory of 165 rays and…
One of the fundamental results in quantum foundations is the Kochen-Specker (KS) theorem, which states that any theory whose predictions agree with quantum mechanics must be contextual, i.e., a quantum observation cannot be understood as…
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…
The Kochen-Specker (KS) theorem is a corner-stone result in the foundations of quantum mechanics describing the fundamental difference between quantum theory and classical non-contextual theories. Recently specific substructures termed…