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This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.<\/jats:p>","DOI":"10.22331\/q-2018-03-30-59","type":"journal-article","created":{"date-parts":[[2018,3,30]],"date-time":"2018-03-30T11:36:28Z","timestamp":1522409788000},"page":"59","source":"Crossref","is-referenced-by-count":12,"title":["Additivity of entropic uncertainty relations"],"prefix":"10.22331","volume":"2","author":[{"given":"Ren\u00e9","family":"Schwonnek","sequence":"first","affiliation":[{"name":"Institut f\u00fcr Theoretische Physik, Leibniz Universit\u00e4t Hannover, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2018,3,30]]},"reference":[{"key":"1","doi-asserted-by":"publisher","unstructured":"J. Schneeloch, C. J. Broadbent, S. P. Walborn, E. G. Cavalcanti, and J. C. Howell. 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