{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T19:36:59Z","timestamp":1775936219064,"version":"3.50.1"},"reference-count":96,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council (formerly Ministry of Science and Technology), Taiwan","award":["107-2112-M006-005-MY2"],"award-info":[{"award-number":["107-2112-M006-005-MY2"]}]},{"name":"National Science and Technology Council (formerly Ministry of Science and Technology), Taiwan","award":["109-2112-M-006-010-MY3"],"award-info":[{"award-number":["109-2112-M-006-010-MY3"]}]},{"name":"National Science and Technology Council (formerly Ministry of Science and Technology), Taiwan","award":["110-2112- M-032-005-MY3"],"award-info":[{"award-number":["110-2112- M-032-005-MY3"]}]},{"name":"National Science and Technology Council (formerly Ministry of Science and Technology), Taiwan","award":["111-2119-M-008-002"],"award-info":[{"award-number":["111-2119-M-008-002"]}]},{"name":"Foundation for Polish Science through the First Team project","award":["First TEAM\/2017-4\/31"],"award-info":[{"award-number":["First TEAM\/2017-4\/31"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>In device-independent quantum information, correlations between local measurement outcomes observed by spatially separated parties in a Bell test play a fundamental role. Even though it is long-known that the set of correlations allowed in quantum theory lies strictly between the Bell-local set and the no-signaling set, many questions concerning the geometry of the quantum set remain unanswered. Here, we revisit the problem of when the boundary of the quantum set coincides with the no-signaling set in the simplest Bell scenario. In particular, for each Class of these common boundaries containing <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi>k<\/mml:mi><\/mml:math> zero probabilities, we provide a <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mn>5<\/mml:mn><mml:mo>&amp;#x2212;<\/mml:mo><mml:mi>k<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>-parameter family of quantum strategies realizing these (extremal) correlations. We further prove that self-testing is possible in all nontrivial Classes beyond the known examples of Hardy-type correlations, and provide numerical evidence supporting the robustness of these self-testing results. Candidates of one-parameter families of self-testing correlations from some of these Classes are identified. As a byproduct of our investigation, if the qubit strategies leading to an extremal nonlocal correlation are local-unitarily equivalent, a self-testing statement provably follows. Interestingly, all these self-testing correlations found on the no-signaling boundary are provably non-exposed. An analogous characterization for the set <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi><\/mml:mrow><\/mml:math> of quantum correlations arising from finite-dimensional maximally entangled states is also provided. En route to establishing this last result, we show that all correlations of <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow class=\"MJX-TeXAtom-ORD\"><mml:mi class=\"MJX-tex-caligraphic\" mathvariant=\"script\">M<\/mml:mi><\/mml:mrow><\/mml:math> in the simplest Bell scenario are attainable as convex combinations of those achievable using a Bell pair and projective measurements. In turn, we obtain the maximal Clauser-Horne-Shimony-Holt Bell inequality violation by any maximally entangled two-qudit state and a no-go theorem regarding the self-testing of such states.<\/jats:p>","DOI":"10.22331\/q-2023-07-11-1054","type":"journal-article","created":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T10:39:06Z","timestamp":1689071946000},"page":"1054","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":14,"title":["Quantum correlations on the no-signaling boundary: self-testing and more"],"prefix":"10.22331","volume":"7","author":[{"given":"Kai-Siang","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gelo Noel M.","family":"Tabia","sequence":"additional","affiliation":[{"name":"Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan"},{"name":"Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan"},{"name":"Center for Quantum Technology, National Tsing Hua University, Hsinchu 300, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jebarathinam","family":"Chellasamy","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotnik\u00f3w 32\/46, 02-668 Warsaw, Poland"},{"name":"Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiladitya","family":"Mal","sequence":"additional","affiliation":[{"name":"Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan"},{"name":"Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun-Yi","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Physics, Tamkang University, Tamsui, New Taipei 251301, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yeong-Cherng","family":"Liang","sequence":"additional","affiliation":[{"name":"Department of Physics and Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University, Tainan 701, Taiwan"},{"name":"Physics Division, National Center for Theoretical Sciences, Taipei 10617, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"S. 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