20.500.12556/RUL-175239 Certifying optimality of Bell inequality violations: noncommutative polynomial optimization through semidefinite programming and local optimization 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. noncommutative polynomial Bell inequality violation Gröbner basis semidefinite programming eigenvalue optimization GNS construction Artin-Wedderburn theory true false true Angleški jezik Ni določen Članek v reviji 2025-10-22 15:09:27 2025-10-22 15:09:31 2025-12-07 04:04:59 0000-00-00 00:00:00 2024 0 0 Str. 1341-1373 iss. 2 Vol. 34 Jun. 2024 0000-00-00 PostprintKoncna Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.8 1052-6234 10.1137/22M1473340 197627907 Hrga,_Klep,_Povh-_Certifying_optimality....pdf Hrga,_Klep,_Povh-_Certifying_optimality....pdf 1 F9BB1CE60EFEC76A6FD622862797D660 893878ef551eb82ccaecbf096894a007174b0d53119bc059d009bd6085503f89 8b94fc2a-af48-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220583 https://epubs.siam.org/doi/10.1137/22M1473340 1 10334e2f-af48-11f0-9328-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=220581 Fakulteta za strojništvo Fakulteta za matematiko in fiziko 0 0 0