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Open AccessArticle

Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces

by Mladen Pavičić 1,2,*,† and Norman D. Megill 3,†
Nano Optics, Department of Physics, Humboldt University, 12489 Berlin, Germany
Center of Excellence for Advanced Materials and Sensors, Research Unit Photonics and Quantum Optics, Institute Ruder Bošković, 10000 Zagreb, Croatia
Boston Information Group, Lexington, MA 02420, USA
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2018, 20(12), 928;
Received: 29 October 2018 / Revised: 21 November 2018 / Accepted: 24 November 2018 / Published: 5 December 2018
(This article belongs to the Special Issue Quantum Probability and Randomness)
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 features. The most elaborated contextual sets, which offer blueprints for contextual experiments and computational gates, are the Kochen–Specker (KS) sets. In this paper, we show a method of vector generation that supersedes previous methods. It is implemented by means of algorithms and programs that generate hypergraphs embodying the Kochen–Specker property and that are designed to be carried out on supercomputers. We show that vector component generation of KS hypergraphs exhausts all possible vectors that can be constructed from chosen vector components, in contrast to previous studies that used incomplete lists of vectors and therefore missed a majority of hypergraphs. Consequently, this unified method is far more efficient for generations of KS sets and their implementation in quantum computation and quantum communication. Several new KS classes and their features have been found and are elaborated on in the paper. Greechie diagrams are discussed. View Full-Text
Keywords: quantum contextuality; Kochen–Specker sets; MMP hypergraphs; Greechie diagrams quantum contextuality; Kochen–Specker sets; MMP hypergraphs; Greechie diagrams
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Pavičić, M.; Megill, N.D. Vector Generation of Quantum Contextual Sets in Even Dimensional Hilbert Spaces. Entropy 2018, 20, 928.

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