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Specifically, we find the minimal energy increase in the system resulting from replacing an entangled pair of modes, sharing entanglement entropy <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mi mathvariant=\"normal\">\u0394<\/mml:mi><mml:mi>S<\/mml:mi><\/mml:math>, by a product state, and we show how to construct modes achieving this minimal energy cost. Thus, we obtain a protocol independent lower bound on the extraction of pure state entanglement from quadratic systems. Due to their generality, our results apply to a large range of physical systems, as we discuss with examples.<\/jats:p>","DOI":"10.22331\/q-2019-07-15-165","type":"journal-article","created":{"date-parts":[[2019,7,15]],"date-time":"2019-07-15T10:01:17Z","timestamp":1563184877000},"page":"165","source":"Crossref","is-referenced-by-count":16,"title":["Minimal energy cost of entanglement extraction"],"prefix":"10.22331","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4172-0317","authenticated-orcid":false,"given":"Lucas","family":"Hackl","sequence":"first","affiliation":[{"name":"Max Planck Institute of Quantum Optics, Hans-Kopfermann-Str. 1, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology, Schellingstra\u00dfe 4, D-80799 M\u00fcnchen, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0295-250X","authenticated-orcid":false,"given":"Robert H.","family":"Jonsson","sequence":"additional","affiliation":[{"name":"QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2019,7,15]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"A. 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