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Article: Violation of all two-party facet Bell inequalities by almost-quantum correlations
Title | Violation of all two-party facet Bell inequalities by almost-quantum correlations |
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Authors | |
Issue Date | 2021 |
Publisher | American Physical Society. The Journal's web site is located at https://journals.aps.org/prresearch/ |
Citation | Physical Review Research, 2021, v. 3 n. 3, p. article no. 033100 How to Cite? |
Abstract | 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. |
Persistent Identifier | http://hdl.handle.net/10722/306565 |
ISSN | 2023 Impact Factor: 3.5 2023 SCImago Journal Rankings: 1.689 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ramanathan, R | - |
dc.date.accessioned | 2021-10-22T07:36:27Z | - |
dc.date.available | 2021-10-22T07:36:27Z | - |
dc.date.issued | 2021 | - |
dc.identifier.citation | Physical Review Research, 2021, v. 3 n. 3, p. article no. 033100 | - |
dc.identifier.issn | 2643-1564 | - |
dc.identifier.uri | http://hdl.handle.net/10722/306565 | - |
dc.description.abstract | 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. | - |
dc.language | eng | - |
dc.publisher | American Physical Society. The Journal's web site is located at https://journals.aps.org/prresearch/ | - |
dc.relation.ispartof | Physical Review Research | - |
dc.rights | Copyright [2021] by The American Physical Society. This article is available online at [http://dx.doi.org/10.1103/PhysRevResearch.3.033100]. | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.title | Violation of all two-party facet Bell inequalities by almost-quantum correlations | - |
dc.type | Article | - |
dc.identifier.email | Ramanathan, R: ravi@cs.hku.hk | - |
dc.identifier.authority | Ramanathan, R=rp02582 | - |
dc.description.nature | published_or_final_version | - |
dc.identifier.doi | 10.1103/PhysRevResearch.3.033100 | - |
dc.identifier.scopus | eid_2-s2.0-85115888432 | - |
dc.identifier.hkuros | 328738 | - |
dc.identifier.volume | 3 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | article no. 033100 | - |
dc.identifier.epage | article no. 033100 | - |
dc.identifier.isi | WOS:000679370800001 | - |
dc.publisher.place | United States | - |