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They can be categorized into three disjoint types: the null-cone, the polystable states and strictly semistable states. Whereas the former two are well characterized, not much is known about strictly semistable states. We derive a criterion for the existence of the latter. In particular, we show that there exists a strictly semistable state if and only if there exist two polystable states whose orbits have different dimensions. We illustrate the usefulness of this criterion by applying it to tripartite states where one of the systems is a qubit. Moreover, we scrutinize all SLOCC classes of these systems and derive a complete characterization of the corresponding orbit types. We present representatives of strictly semistable classes and show to which polystable state they converge via local regular operators.<\/jats:p>","DOI":"10.22331\/q-2020-07-20-300","type":"journal-article","created":{"date-parts":[[2020,7,20]],"date-time":"2020-07-20T10:47:17Z","timestamp":1595242037000},"page":"300","source":"Crossref","is-referenced-by-count":7,"title":["A link between symmetries of critical states and the structure of SLOCC classes in multipartite systems"],"prefix":"10.22331","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4138-3063","authenticated-orcid":false,"given":"Oskar","family":"S\u0142owik","sequence":"first","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5841-7082","authenticated-orcid":false,"given":"Martin","family":"Hebenstreit","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, University of Innsbruck, A\u20136020 Innsbruck, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7246-6385","authenticated-orcid":false,"given":"Barbara","family":"Kraus","sequence":"additional","affiliation":[{"name":"Institute for Theoretical Physics, University of Innsbruck, A\u20136020 Innsbruck, Austria"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4906-2459","authenticated-orcid":false,"given":"Adam","family":"Sawicki","sequence":"additional","affiliation":[{"name":"Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland"}]}],"member":"9598","published-online":{"date-parts":[[2020,7,20]]},"reference":[{"key":"0","doi-asserted-by":"crossref","unstructured":"M. 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