Hexagons govern three-qubit contextuality
Split Cayley hexagons of order two are distinguished finite geometries living in the three-qubit symplectic polar space in two different forms, called classical and skew. Although neither of the two yields observable-based contextual configurations of their own, $classically$-embedded copies are fo...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-01-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-01-20-1601/pdf/ |
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| author | Metod Saniga Frédéric Holweck Colm Kelleher Axel Muller Alain Giorgetti Henri de Boutray |
| author_facet | Metod Saniga Frédéric Holweck Colm Kelleher Axel Muller Alain Giorgetti Henri de Boutray |
| author_sort | Metod Saniga |
| collection | DOAJ |
| description | Split Cayley hexagons of order two are distinguished finite geometries living in the three-qubit symplectic polar space in two different forms, called classical and skew. Although neither of the two yields observable-based contextual configurations of their own, $classically$-embedded copies are found to fully encode contextuality properties of the most prominent three-qubit contextual configurations in the following sense: for each set of unsatisfiable contexts of such a contextual configuration there exists some classically-embedded hexagon sharing with the configuration exactly this set of contexts and nothing else. We demonstrate this fascinating property first on the configuration comprising all 315 contexts of the space and then on doilies, both types of quadrics as well as on complements of skew-embedded hexagons. In connection with the last-mentioned case and elliptic quadrics we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to substantiate our theoretical findings. |
| format | Article |
| id | doaj-art-a674ed7b54024839996b97241e00351d |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-a674ed7b54024839996b97241e00351d2025-01-23T16:41:01ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-01-019160110.22331/q-2025-01-20-160110.22331/q-2025-01-20-1601Hexagons govern three-qubit contextualityMetod SanigaFrédéric HolweckColm KelleherAxel MullerAlain GiorgettiHenri de BoutraySplit Cayley hexagons of order two are distinguished finite geometries living in the three-qubit symplectic polar space in two different forms, called classical and skew. Although neither of the two yields observable-based contextual configurations of their own, $classically$-embedded copies are found to fully encode contextuality properties of the most prominent three-qubit contextual configurations in the following sense: for each set of unsatisfiable contexts of such a contextual configuration there exists some classically-embedded hexagon sharing with the configuration exactly this set of contexts and nothing else. We demonstrate this fascinating property first on the configuration comprising all 315 contexts of the space and then on doilies, both types of quadrics as well as on complements of skew-embedded hexagons. In connection with the last-mentioned case and elliptic quadrics we also conducted some experimental tests on a Noisy Intermediate Scale Quantum (NISQ) computer to substantiate our theoretical findings.https://quantum-journal.org/papers/q-2025-01-20-1601/pdf/ |
| spellingShingle | Metod Saniga Frédéric Holweck Colm Kelleher Axel Muller Alain Giorgetti Henri de Boutray Hexagons govern three-qubit contextuality Quantum |
| title | Hexagons govern three-qubit contextuality |
| title_full | Hexagons govern three-qubit contextuality |
| title_fullStr | Hexagons govern three-qubit contextuality |
| title_full_unstemmed | Hexagons govern three-qubit contextuality |
| title_short | Hexagons govern three-qubit contextuality |
| title_sort | hexagons govern three qubit contextuality |
| url | https://quantum-journal.org/papers/q-2025-01-20-1601/pdf/ |
| work_keys_str_mv | AT metodsaniga hexagonsgovernthreequbitcontextuality AT fredericholweck hexagonsgovernthreequbitcontextuality AT colmkelleher hexagonsgovernthreequbitcontextuality AT axelmuller hexagonsgovernthreequbitcontextuality AT alaingiorgetti hexagonsgovernthreequbitcontextuality AT henrideboutray hexagonsgovernthreequbitcontextuality |