Non-locality, contextuality and valuation algebras: a general theory of disagreement
We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equiva...
| Main Authors: | , |
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| Format: | Journal article |
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Royal Society
2019
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| _version_ | 1826266500746444800 |
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| author | Abramsky, S Caru, G |
| author_facet | Abramsky, S Caru, G |
| author_sort | Abramsky, S |
| collection | OXFORD |
| description | We establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equivalent to a general notion of disagreement between information sources. This result vastly generalises previously observed connections between contextuality, relationaldatabases, constraint satisfaction problems, and logical paradoxes, and gives further proof that contextual behaviour is not a phenomenon limited to quantum physics, but pervades various domains of mathematics and computer science. The connection allows to translate theorems, methods and algorithms from one field to the other, and paves the way for the application of generic inference algorithms to study contextuality. |
| first_indexed | 2024-03-06T20:39:54Z |
| format | Journal article |
| id | oxford-uuid:33ec89eb-2930-4ebe-895a-a136d6fda905 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:39:54Z |
| publishDate | 2019 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:33ec89eb-2930-4ebe-895a-a136d6fda9052022-03-26T13:22:57ZNon-locality, contextuality and valuation algebras: a general theory of disagreementJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:33ec89eb-2930-4ebe-895a-a136d6fda905Symplectic Elements at OxfordRoyal Society2019Abramsky, SCaru, GWe establish a strong link between two apparently unrelated topics: the study of conflicting information in the formal framework of valuation algebras, and the phenomena of non-locality and contextuality. In particular, we show that these peculiar features of quantum theory are mathematically equivalent to a general notion of disagreement between information sources. This result vastly generalises previously observed connections between contextuality, relationaldatabases, constraint satisfaction problems, and logical paradoxes, and gives further proof that contextual behaviour is not a phenomenon limited to quantum physics, but pervades various domains of mathematics and computer science. The connection allows to translate theorems, methods and algorithms from one field to the other, and paves the way for the application of generic inference algorithms to study contextuality. |
| spellingShingle | Abramsky, S Caru, G Non-locality, contextuality and valuation algebras: a general theory of disagreement |
| title | Non-locality, contextuality and valuation algebras: a general theory of disagreement |
| title_full | Non-locality, contextuality and valuation algebras: a general theory of disagreement |
| title_fullStr | Non-locality, contextuality and valuation algebras: a general theory of disagreement |
| title_full_unstemmed | Non-locality, contextuality and valuation algebras: a general theory of disagreement |
| title_short | Non-locality, contextuality and valuation algebras: a general theory of disagreement |
| title_sort | non locality contextuality and valuation algebras a general theory of disagreement |
| work_keys_str_mv | AT abramskys nonlocalitycontextualityandvaluationalgebrasageneraltheoryofdisagreement AT carug nonlocalitycontextualityandvaluationalgebrasageneraltheoryofdisagreement |