Violation of all two-party facet Bell inequalities by almost-quantum correlations
The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in quantum theory is an intriguing one in this regard. Here we make significant progress in answering this ques...
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.033100 |
| _version_ | 1797211026354077696 |
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| author | Ravishankar Ramanathan |
| author_facet | Ravishankar Ramanathan |
| author_sort | Ravishankar Ramanathan |
| collection | DOAJ |
| description | The characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in quantum theory is an intriguing one in this regard. Here we make significant progress in answering this question, by showing that every tight Bell inequality is violated by “almost-quantum” correlations, a semidefinite programming relaxation of the set of quantum correlations. As a consequence, we show that many (classes of) Bell inequalities including two-party correlation Bell inequalities and multioutcome nonlocal computation games, which do not admit quantum violations, are not facets of the classical Bell polytope. To do this, we make use of the intriguing connections between Bell correlations and the graph-theoretic Lovász-theta set, discovered by Cabello-Severini-Winter (CSW). We also exploit connections between the cut polytope of graph theory and the classical correlation Bell polytope, to show that correlation Bell inequalities that define facets of the lower dimensional correlation polytope are violated in quantum theory. |
| first_indexed | 2024-04-24T10:19:56Z |
| format | Article |
| id | doaj.art-e872ab970fd54cac87c2622923166cef |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:19:56Z |
| publishDate | 2021-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-e872ab970fd54cac87c2622923166cef2024-04-12T17:12:21ZengAmerican Physical SocietyPhysical Review Research2643-15642021-07-013303310010.1103/PhysRevResearch.3.033100Violation of all two-party facet Bell inequalities by almost-quantum correlationsRavishankar RamanathanThe characterization of the set of quantum correlations is a problem of fundamental importance in quantum information. The question whether every proper (tight) Bell inequality is violated in quantum theory is an intriguing one in this regard. Here we make significant progress in answering this question, by showing that every tight Bell inequality is violated by “almost-quantum” correlations, a semidefinite programming relaxation of the set of quantum correlations. As a consequence, we show that many (classes of) Bell inequalities including two-party correlation Bell inequalities and multioutcome nonlocal computation games, which do not admit quantum violations, are not facets of the classical Bell polytope. To do this, we make use of the intriguing connections between Bell correlations and the graph-theoretic Lovász-theta set, discovered by Cabello-Severini-Winter (CSW). We also exploit connections between the cut polytope of graph theory and the classical correlation Bell polytope, to show that correlation Bell inequalities that define facets of the lower dimensional correlation polytope are violated in quantum theory.http://doi.org/10.1103/PhysRevResearch.3.033100 |
| spellingShingle | Ravishankar Ramanathan Violation of all two-party facet Bell inequalities by almost-quantum correlations Physical Review Research |
| title | Violation of all two-party facet Bell inequalities by almost-quantum correlations |
| title_full | Violation of all two-party facet Bell inequalities by almost-quantum correlations |
| title_fullStr | Violation of all two-party facet Bell inequalities by almost-quantum correlations |
| title_full_unstemmed | Violation of all two-party facet Bell inequalities by almost-quantum correlations |
| title_short | Violation of all two-party facet Bell inequalities by almost-quantum correlations |
| title_sort | violation of all two party facet bell inequalities by almost quantum correlations |
| url | http://doi.org/10.1103/PhysRevResearch.3.033100 |
| work_keys_str_mv | AT ravishankarramanathan violationofalltwopartyfacetbellinequalitiesbyalmostquantumcorrelations |