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In this work, we completely characterize universal embezzling families and demonstrate how this singles out the original family introduced by van Dam and Hayden. To achieve this, we first give a full characterization of pure to mixed state LOCC-conversions. Then, we introduce a new conversion distance and derive a closed-form expression for it. These results might be of independent interest.<\/jats:p>","DOI":"10.22331\/q-2024-06-13-1368","type":"journal-article","created":{"date-parts":[[2024,6,13]],"date-time":"2024-06-13T14:07:27Z","timestamp":1718287647000},"page":"1368","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":8,"title":["Complete Characterization of Entanglement Embezzlement"],"prefix":"10.22331","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-7494-2968","authenticated-orcid":false,"given":"Elia","family":"Zanoni","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada"},{"name":"Institute for Quantum Science and Technology, University of Calgary, Calgary, AB T2N 1N4, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3888-4628","authenticated-orcid":false,"given":"Thomas","family":"Theurer","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada"},{"name":"Institute for Quantum Science and Technology, University of Calgary, Calgary, AB T2N 1N4, Canada"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4892-4072","authenticated-orcid":false,"given":"Gilad","family":"Gour","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada"},{"name":"Institute for Quantum Science and Technology, University of Calgary, Calgary, AB T2N 1N4, Canada"}]}],"member":"9598","published-online":{"date-parts":[[2024,6,13]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Charles H. 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