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In particular, we show that the maximal violation of an arbitrary unbiased dichotomic steering inequality is given by the inclusion constants of the matrix cube, which is a well-studied object in convex optimization theory. This allows us to find new upper bounds on the maximal violation of steering inequalities and to show that previously obtained violations are optimal. In order to do this, we prove lower bounds on the inclusion constants of the complex matrix cube, which might be of independent interest. Finally, we show that the inclusion constants of the matrix cube and the matrix diamond are the same. This allows us to derive new bounds on the amount of incompatibility available in dichotomic quantum measurements in fixed dimension.<\/jats:p>","DOI":"10.22331\/q-2022-02-21-656","type":"journal-article","created":{"date-parts":[[2022,2,21]],"date-time":"2022-02-21T12:11:45Z","timestamp":1645445505000},"page":"656","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Maximal violation of steering inequalities and the matrix cube"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4796-7633","authenticated-orcid":false,"given":"Andreas","family":"Bluhm","sequence":"first","affiliation":[{"name":"QMATH, Department of Mathematical Sciences, University of Copenhagen, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3016-7795","authenticated-orcid":false,"given":"Ion","family":"Nechita","sequence":"additional","affiliation":[{"name":"Laboratoire de Physique Th\u00e9orique, Universit\u00e9 de Toulouse, CNRS, UPS, France"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,2,21]]},"reference":[{"key":"0","unstructured":"NIST digital library of mathematical functions. http:\/\/dlmf.nist.gov\/, Release 1.1.1 of 2021-03-15. 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