{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T16:50:41Z","timestamp":1759942241911,"version":"3.41.2"},"reference-count":34,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","funder":[{"name":"Portuguese Science Foundation","award":["PTDC\/MATCAL\/4334\/2014"],"award-info":[{"award-number":["PTDC\/MATCAL\/4334\/2014"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Rev. Math. Phys."],"published-print":{"date-parts":[[2022,4]]},"abstract":"<jats:p>The notion of partial trace of a density operator is essential for the understanding of the entanglement and separability properties of quantum states. In this paper, we investigate these notions putting an emphasis on the geometrical properties of the covariance ellipsoids of the reduced states. We thereafter focus on Gaussian states and we give new and easily numerically implementable sufficient conditions for the separability of all Gaussian states. Unlike the positive partial transposition criterion, none of these conditions is however necessary.<\/jats:p>","DOI":"10.1142\/s0129055x22500052","type":"journal-article","created":{"date-parts":[[2021,11,9]],"date-time":"2021-11-09T09:49:21Z","timestamp":1636451361000},"source":"Crossref","is-referenced-by-count":3,"title":["Partial traces and the geometry of entanglement: Sufficient conditions for the separability of Gaussian states"],"prefix":"10.1142","volume":"34","author":[{"given":"Nuno Costa","family":"Dias","sequence":"first","affiliation":[{"name":"Grupo de F\u00edsica Matem\u00e1tica, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade de Lisboa, Campo Grande, Edif\u00edcio C6, 1749-016 Lisboa, Portugal"},{"name":"Escola Superior N\u00e1utica Infante D. Henrique, Avenida Engenheiro Bonneville Franco, 2770-058 Pa\u00e7o de Arcos, Portugal"}]},{"given":"Maurice","family":"de Gosson","sequence":"additional","affiliation":[{"name":"Numerical Harmonic Analysis Group (NuHAG), Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria"}]},{"given":"Jo\u00e3o Nuno","family":"Prata","sequence":"additional","affiliation":[{"name":"Grupo de F\u00edsica Matem\u00e1tica, Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade de Lisboa, Campo Grande, Edif\u00edcio C6, 1749-016 Lisboa, Portugal"},{"name":"Escola Superior N\u00e1utica Infante D. Henrique, Avenida Engenheiro Bonneville Franco, 2770-058 Pa\u00e7o de Arcos, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2021,11,9]]},"reference":[{"key":"S0129055X22500052BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S1793525313500015"},{"key":"S0129055X22500052BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-015-0832-3"},{"key":"S0129055X22500052BIB003","doi-asserted-by":"publisher","DOI":"10.1364\/JOSA.69.001710"},{"key":"S0129055X22500052BIB004","doi-asserted-by":"publisher","DOI":"10.1515\/9781400881994"},{"key":"S0129055X22500052BIB007","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.2722"},{"issue":"1","key":"S0129055X22500052BIB008","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/BF02845227","volume":"16","author":"Du J.","year":"2000","journal-title":"Approx. Theory Appl. (N.S.)"},{"key":"S0129055X22500052BIB009","doi-asserted-by":"publisher","DOI":"10.1515\/9781400882427"},{"key":"S0129055X22500052BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/3-7643-7575-2"},{"key":"S0129055X22500052BIB012","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-009-9272-2"},{"key":"S0129055X22500052BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7643-9992-4"},{"key":"S0129055X22500052BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s10701-012-9636-x"},{"key":"S0129055X22500052BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/q0089"},{"key":"S0129055X22500052BIB016","doi-asserted-by":"publisher","DOI":"10.12743\/quanta.v7i1.74"},{"key":"S0129055X22500052BIB017","doi-asserted-by":"publisher","DOI":"10.1016\/j.physrep.2009.08.001"},{"key":"S0129055X22500052BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388806"},{"volume-title":"Matrix Analysis","year":"1990","author":"Horn R. A.","key":"S0129055X22500052BIB019"},{"key":"S0129055X22500052BIB020","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(96)00706-2"},{"key":"S0129055X22500052BIB021","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00142-6"},{"key":"S0129055X22500052BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/BF01649588"},{"key":"S0129055X22500052BIB023","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aaa654"},{"key":"S0129055X22500052BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/BF01773339"},{"issue":"1","key":"S0129055X22500052BIB025","first-page":"39","volume":"6","author":"Loupias G.","year":"1967","journal-title":"Ann. Inst. H. Poincar\u00e9"},{"key":"S0129055X22500052BIB026","doi-asserted-by":"publisher","DOI":"10.1063\/1.528537"},{"key":"S0129055X22500052BIB027","doi-asserted-by":"publisher","DOI":"10.1063\/1.528922"},{"key":"S0129055X22500052BIB028","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.34.1"},{"key":"S0129055X22500052BIB029","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.77.1413"},{"key":"S0129055X22500052BIB030","doi-asserted-by":"publisher","DOI":"10.1201\/9781315118727"},{"key":"S0129055X22500052BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-96854-9"},{"key":"S0129055X22500052BIB032","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.84.2726"},{"key":"S0129055X22500052BIB033","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.36.3868"},{"key":"S0129055X22500052BIB034","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(01)00278-4"},{"key":"S0129055X22500052BIB035","doi-asserted-by":"publisher","DOI":"10.1063\/1.526310"},{"key":"S0129055X22500052BIB036","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.86.3658"},{"key":"S0129055X22500052BIB037","doi-asserted-by":"publisher","DOI":"10.1007\/b105056"}],"container-title":["Reviews in Mathematical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129055X22500052","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T11:48:54Z","timestamp":1699789734000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129055X22500052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,9]]},"references-count":34,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2022,4]]}},"alternative-id":["10.1142\/S0129055X22500052"],"URL":"https:\/\/doi.org\/10.1142\/s0129055x22500052","relation":{},"ISSN":["0129-055X","1793-6659"],"issn-type":[{"type":"print","value":"0129-055X"},{"type":"electronic","value":"1793-6659"}],"subject":[],"published":{"date-parts":[[2021,11,9]]},"article-number":"2250005"}}