Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910981029888000 |
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| author | Williams, Tom Constantin, Andrei |
| author_facet | Williams, Tom Constantin, Andrei |
| contents | The challenge of determining bounds for the minimal number of vectors in a three-dimensional Kochen-Specker (KS) set has captivated the quantum foundations community for decades. This paper establishes a weak lower bound of 10 vectors, which does not surpass the current best-known bound of 24 vectors. By exploring the complementary concept of large non-KS sets and employing a probability argument independent of the graph structure of KS sets, we introduce a novel technique that could be applied in the future to derive tighter bounds. Additionally, we highlight an intriguing connection to a generalisation of the moving sofa problem in navigating a right-angled hallway on the surface of a two-dimensional sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_05230 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets Williams, Tom Constantin, Andrei Quantum Physics Discrete Mathematics Metric Geometry The challenge of determining bounds for the minimal number of vectors in a three-dimensional Kochen-Specker (KS) set has captivated the quantum foundations community for decades. This paper establishes a weak lower bound of 10 vectors, which does not surpass the current best-known bound of 24 vectors. By exploring the complementary concept of large non-KS sets and employing a probability argument independent of the graph structure of KS sets, we introduce a novel technique that could be applied in the future to derive tighter bounds. Additionally, we highlight an intriguing connection to a generalisation of the moving sofa problem in navigating a right-angled hallway on the surface of a two-dimensional sphere. |
| title | Maximal Non-Kochen-Specker Sets and a Lower Bound on the Size of Kochen-Specker Sets |
| topic | Quantum Physics Discrete Mathematics Metric Geometry |
| url | https://arxiv.org/abs/2403.05230 |