https://doi.org/10.1051/epjconf/201919800009
Vector generation of contextual sets
1
Nano Optics, Department of Physics, Humboldt University (HU), Berlin, Germany
2
Center of Excellence for Advanced Materials and Sensors (CEMS), Research Unit Photonics and Quantum Optics, Institute Ruder Bošković (IRB), Zagreb, Croatia
3
Boston Information Group (BIG), Lexington, MA 02420, U.S.A.
* e-mail: mpavicic@irb.hr
Published online: 15 January 2019
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 three previous methods: (i) fortuitous discoveries of smallest KS sets, (ii) exhaustive upward hypergraph-generation of sets, and (iii) random downward generation of sets from fortuitously obtained big master sets. In contrast to previous works, we can generate master sets which contain all possible KS sets starting with nothing but a few simple vector components. From them we can readily generate all KS sets obtained in the last half a century and any specified new KS sets. Herewith we can generate sufficiently large sets as well as sets with definite required features and structures to enable varieties of different implementations in quantum computation and communication.
© The Authors, published by EDP Sciences, 2019
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
