{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814801,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We investigate separability of Laplacian matrices of graphs when seen as density matrices. This is a family of quantum states with many combinatorial properties. We firstly show that the well-known matrix realignment criterion can be used to test separability of this type of quantum states. The criterion can be interpreted as novel graph-theoretic idea. Then, we prove that the density matrix of the tensor product of N graphs is N-separable. However, the converse is not necessarily true.\u00a0Additionally, we derive a sufficient condition for N-partite entanglement in star graphs and propose a necessary and sufficient condition for separability of nearest point graphs.<\/jats:p>","DOI":"10.37236\/3092","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:12:39Z","timestamp":1578705159000},"source":"Crossref","is-referenced-by-count":4,"title":["Separability of Density Matrices of Graphs for Multipartite Systems"],"prefix":"10.37236","volume":"20","author":[{"given":"Chen","family":"Xie","sequence":"first","affiliation":[]},{"given":"Hui","family":"Zhao","sequence":"additional","affiliation":[]},{"given":"Zhixi","family":"Wang","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,11,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p21\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i4p21\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:10:59Z","timestamp":1579259459000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i4p21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,22]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,10,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3092","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,11,22]]},"article-number":"P21"}}