The logical structure of contextuality and nonclassicality
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918226714165248 |
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| author | Liu, Songyi Wang, Yongjun Wang, Baoshan He, Chang Wang, Jincheng |
| author_facet | Liu, Songyi Wang, Yongjun Wang, Baoshan He, Chang Wang, Jincheng |
| contents | Quantum contextuality represents a fundamental form of nonclassicality in quantum mechanics. To provide a more complete characterization of nonclassical properties in quantum systems, we adopt a logical perspective and propose a mathematical framework based on exclusive partial Boolean algebras (epBAs). This framework enables a unified description of contextuality and nonclassicality across finite general, quantum, and classical systems. We establish a unified and minimal classical counterpart for any finite general system. Within this framework, we formalize major categories of quantum contextuality, demonstrating that: 12 projectors suffice to generate Kochen-Specker scenarios; 10 projectors suffice to witness state-independent contextuality; and 3 observables suffice to witness quantum contextuality. Finally, we prove that contextuality is a sufficient but not necessary condition for nonclassicality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15071 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The logical structure of contextuality and nonclassicality Liu, Songyi Wang, Yongjun Wang, Baoshan He, Chang Wang, Jincheng Quantum Physics Quantum contextuality represents a fundamental form of nonclassicality in quantum mechanics. To provide a more complete characterization of nonclassical properties in quantum systems, we adopt a logical perspective and propose a mathematical framework based on exclusive partial Boolean algebras (epBAs). This framework enables a unified description of contextuality and nonclassicality across finite general, quantum, and classical systems. We establish a unified and minimal classical counterpart for any finite general system. Within this framework, we formalize major categories of quantum contextuality, demonstrating that: 12 projectors suffice to generate Kochen-Specker scenarios; 10 projectors suffice to witness state-independent contextuality; and 3 observables suffice to witness quantum contextuality. Finally, we prove that contextuality is a sufficient but not necessary condition for nonclassicality. |
| title | The logical structure of contextuality and nonclassicality |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.15071 |