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Any 'a priori' constraint for the properties of the global vs. the local states-the so-called marginals-would help in order to narrow down the wealth of possible solutions for a given many-body problem, however, little is known about such constraints. We derive an equality for correlation-related quantities of any multipartite quantum system composed of finite-dimensional local parties. This relation defines a necessary condition for the compatibility of the marginal properties with those of the joint state. While the equality holds both for pure and mixed states, the pure-state version containing only entanglement measures represents a fully general monogamy relation for entanglement. These findings have interesting implications in terms of conservation laws for correlations, and also with respect to topology.<\/jats:p>","DOI":"10.22331\/q-2018-05-22-64","type":"journal-article","created":{"date-parts":[[2018,5,22]],"date-time":"2018-05-22T12:03:47Z","timestamp":1526990627000},"page":"64","source":"Crossref","is-referenced-by-count":27,"title":["Distribution of entanglement and correlations in all finite dimensions"],"prefix":"10.22331","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9428-5593","authenticated-orcid":false,"given":"Christopher","family":"Eltschka","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Universit\u00e4t Regensburg, D-93040 Regensburg, Germany"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9410-5043","authenticated-orcid":false,"given":"Jens","family":"Siewert","sequence":"additional","affiliation":[{"name":"Departamento de Qu\u00edmica F\u00edsica, Universidad del Pa\u00eds Vasco UPV\/EHU, E-48080 Bilbao, Spain"},{"name":"IKERBASQUE Basque Foundation for Science, E-48013 Bilbao, Spain"}]}],"member":"9598","published-online":{"date-parts":[[2018,5,22]]},"reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"E. 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