Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions
Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specifi...
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MDPI AG
2025-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/54 |
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| author | Mladen Pavičić |
| author_facet | Mladen Pavičić |
| author_sort | Mladen Pavičić |
| collection | DOAJ |
| description | Quantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field. |
| format | Article |
| id | doaj-art-ec923824168f4d928ee597625b122cee |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-ec923824168f4d928ee597625b122cee2025-01-24T13:31:49ZengMDPI AGEntropy1099-43002025-01-012715410.3390/e27010054Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher DimensionsMladen Pavičić0Center of Excellence for Advanced Materials and Sensors, Research Unit Photonics and Quantum Optics, Institute Ruder Bošković, 10000 Zagreb, CroatiaQuantum contextuality plays a significant role in supporting quantum computation and quantum information theory. The key tools for this are the Kochen–Specker and non-Kochen–Specker contextual sets. Traditionally, their representation has been predominantly operator-based, mainly focusing on specific constructs in dimensions ranging from three to eight. However, nearly all of these constructs can be represented as low-dimensional hypergraphs. This study demonstrates how to generate contextual hypergraphs in any dimension using various methods, particularly those that do not scale in complexity with increasing dimensions. Furthermore, we introduce innovative examples of hypergraphs extending to dimension 32. Our methodology reveals the intricate structural properties of hypergraphs, enabling precise quantifications of contextuality. Additionally, we investigate several promising applications of hypergraphs in quantum communication and quantum computation, paving the way for future breakthroughs in the field.https://www.mdpi.com/1099-4300/27/1/54quantum contextualityhypergraph contextualityMMP hypergraphsoperator contextualityrandom generationKochen–Specker sets |
| spellingShingle | Mladen Pavičić Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions Entropy quantum contextuality hypergraph contextuality MMP hypergraphs operator contextuality random generation Kochen–Specker sets |
| title | Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions |
| title_full | Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions |
| title_fullStr | Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions |
| title_full_unstemmed | Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions |
| title_short | Quantum Contextual Hypergraphs, Operators, Inequalities, and Applications in Higher Dimensions |
| title_sort | quantum contextual hypergraphs operators inequalities and applications in higher dimensions |
| topic | quantum contextuality hypergraph contextuality MMP hypergraphs operator contextuality random generation Kochen–Specker sets |
| url | https://www.mdpi.com/1099-4300/27/1/54 |
| work_keys_str_mv | AT mladenpavicic quantumcontextualhypergraphsoperatorsinequalitiesandapplicationsinhigherdimensions |