Non-Kochen-Specker Contextuality
arXiv:2307.16339 · doi:10.3390/e25081117
Abstract
Quantum contextuality supports quantum computation and communication. One of its main vehicles is hypergraphs. The most elaborated are the Kochen-Specker ones, but there is also another class of contextual sets that are not of this kind. Their representation has been mostly operator-based and limited to special constructs in three- to six-dim spaces, a notable example of which is the Yu-Oh set. Previously, we showed that hypergraphs underlie all of them, and in this paper, we give general methods - whose complexity does not scale up with the dimension - for generating such non-Kochen-Specker hypergraphs in any dimension and give examples in up to 16-dim spaces. Our automated generation is probabilistic and random, but the statistics of accumulated data enable one to filter out sets with the required size and structure.
arXiv comment19 pages, 5 figures, 1 table; 8-dim part of Fig. 3 has been corrected ((h) and (i) are not isomorphic); Nothing else in the rest of the paper is affected by this correction; The correction is published in Entropy 2024, 26(2), 100; https://doi.org/10.3390/e26020100
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