Non-Kochen-Specker Contextuality
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914797490012160 |
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| author | Pavicic, Mladen |
| author_facet | Pavicic, Mladen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16339 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-Kochen-Specker Contextuality Pavicic, Mladen Quantum Physics Mathematical Physics 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. |
| title | Non-Kochen-Specker Contextuality |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2307.16339 |