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Certifying optimality of Bell inequality violations: noncommutative polynomial optimization through semidefinite programming and local optimizationHrga, Timotej ; Klep, Igor, matematik ; Povh, Janez, 1973-Bell inequalities are pillars of quantum physics in that their violations imply that certain properties of quantum physics (e.g., entanglement) cannot be represented by any classical picture of ... physics. In this article Bell inequalities and their violations are considered through the lens of noncommutative polynomial optimization. Optimality of these violations is certified for a large majority of a set of standard Bell inequalities, denoted A2-A89 in the literature. The main techniques used in the paper include the NPA hierarchy, i.e., the noncommutative version of the Lasserre semidefinite programming (SDP) hierarchies based on the Helton-McCullough Positivstellensatz,the Gelfand-Naimark-Segal (GNS) construction with a novel use of the Artin-Wedderburn theory for rounding and projecting, and nonlinear programming (NLP). A new "Newton chip"-like technique for reducing sizes of SDPs arising in the constructed polynomial optimization problems is presented.This technique is based on conditional expectations. Finally, noncommutative Gröbner bases are exploited to certify when an optimizer (a solution yielding optimum violation) cannot be extracted from a dual SDP solution.Source: SIAM journal on optimization. - ISSN 1052-6234 (Vol. 34, iss. 2, Jun. 2024, str. 1341-1373)Type of material - article, component part ; adult, seriousPublish date - 2024Language - englishCOBISS.SI-ID - 197627907
Digital content: dCOBISS
| Author | Hrga, Timotej ; Klep, Igor, matematik ; Povh, Janez, 1973- |
| Title | Certifying optimality of Bell inequality violations: noncommutative polynomial optimization through semidefinite programming and local optimization |
| Publication date | 2024-04-09 |
| COBISS.SI-ID | 197627907 |
| Publication version in repository | Postprint, author's finally reviewed version, accepted for publication |
| Publication licence | Creative Commons Attribution 4.0 International |
| Embargo | Immediate publication for public |
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| Algebra, teorija operatorjev in finančna matematika | P1-0222-2022 |
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| QuantERA II ERA-NET Cofund in Quantum Technologies | QuantERA II | 101017733 |
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| Večfazni sistemi | P2-0162-2022 |
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| Napovedovanje sodelovanja med raziskovalci s pomočjo odkrivanja zakonitosti iz literature | J5-2552-2020 |
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| Razširitev algoritmov prvega in drugega reda za izbrane razrede optimizacijskih problemov s ciljem rešiti računsko zahtevne industrijske probleme | N1-0071-2017 |
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Files that belong to the publication
| Link |
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https://epubs.siam.org/doi/10.1137/22M1473340
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https://d.cobiss.net/repository/si/files/197627907/157542/Hrga_Klep_Povh_v3.pdf
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