Related papers: Non-Kochen-Specker Contextuality
Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen--Specker and non-Kochen--Specker contextual sets. Traditionally, their representation has…
Quantum contextuality is a source of quantum computational power and a theoretical delimiter between classical and quantum structures. It has been substantiated by numerous experiments and prompted generation of state independent contextual…
As quantum contextuality proves to be a necessary resource for universal quantum computation, we present a general method for vector generation of Kochen-Specker (KS) contextual sets in the form of hypergraphs. The method supersedes all…
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…
Quantum contextuality turns out to be a necessary resource for universal quantum computation and important in the field of quantum information processing. It is therefore of interest both for theoretical considerations and for experimental…
Quantum contextual sets have been recognized as resources for universal quantum computation, quantum steering and quantum communication. Therefore, we focus on engineering the sets that support those resources and on determining their…
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…
Quantum contextuality turns out to be a necessary resource for universal quantum computation and also has applications in quantum communication. Thus it becomes important to generate contextual sets of arbitrary structure and complexity to…
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…
This article delves into the concept of quantum contextuality, specifically focusing on proofs of the Kochen-Specker theorem obtained by assigning Pauli observables to hypergraph vertices satisfying a given commutation relation. The…
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…
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…
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…
One of the interesting topics in quantum contextuality is the construction for various non-contextual inequalities. By introducing a new structure called hyper-graph, we present a general method, which seems to be analytic and extensible,…
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…
We give a method for exhaustive generation of a huge number of Kochen-Specker contextual sets, based on the 600-cell, for possible experiments and quantum gates. The method is complementary to our previous parity proof generation of these…
We introduce a contextual quantum system comprising mutually complementary observables organized into two or more collections of pseudocontexts with the same probability sums of outcomes. These pseudocontexts constitute non-orthogonal bases…
The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D.…
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…
Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…