{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T20:56:38Z","timestamp":1778792198847,"version":"3.51.4"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,3,2]],"date-time":"2018-03-02T00:00:00Z","timestamp":1519948800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Ministry of Science and Technology of the Peoples\u2019 Republic of China","award":["2015CB856703"],"award-info":[{"award-number":["2015CB856703"]}]},{"name":"Strategic Priority Research Program of the Chinese Academy of Sciences","award":["XDB23030100"],"award-info":[{"award-number":["XDB23030100"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11375200"],"award-info":[{"award-number":["11375200"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11635009"],"award-info":[{"award-number":["11635009"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2018,4]]},"DOI":"10.1007\/s11128-018-1862-5","type":"journal-article","created":{"date-parts":[[2018,3,1]],"date-time":"2018-03-01T20:51:56Z","timestamp":1519937516000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Separable decompositions of bipartite mixed states"],"prefix":"10.1007","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4742-8090","authenticated-orcid":false,"given":"Jun-Li","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cong-Feng","family":"Qiao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,2]]},"reference":[{"key":"1862_CR1","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielsen","year":"2000","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"key":"1862_CR2","doi-asserted-by":"publisher","first-page":"4277","DOI":"10.1103\/PhysRevA.40.4277","volume":"40","author":"RF Werner","year":"1989","unstructured":"Werner, R.F.: Quantum states with Einstein\u2013Podolsky\u2013Rosen correlations admitting a hidden-variable model. Phys. Rev. A 40, 4277\u20134281 (1989)","journal-title":"Phys. Rev. A"},{"key":"1862_CR3","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1016\/j.jcss.2004.06.003","volume":"69","author":"L Gurvits","year":"2004","unstructured":"Gurvits, L.: Classical complexity and quantum entanglement. J. Comput. Syst. Sci. 69, 448\u2013484 (2004)","journal-title":"J. Comput. Syst. Sci."},{"key":"1862_CR4","doi-asserted-by":"publisher","first-page":"1413","DOI":"10.1103\/PhysRevLett.77.1413","volume":"77","author":"A Peres","year":"1996","unstructured":"Peres, A.: Separability criterion for density matrices. Phys. Rev. Lett. 77, 1413\u20131415 (1996)","journal-title":"Phys. Rev. Lett."},{"key":"1862_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0375-9601(96)00706-2","volume":"223","author":"M Horodecki","year":"1996","unstructured":"Horodecki, M., Horodecki, P., Horodecki, R.: Separability of mixed states: necessary and sufficient conditions. Phys. Lett. A 223, 1\u20138 (1996)","journal-title":"Phys. Lett. A"},{"key":"1862_CR6","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s11128-005-5664-1","volume":"4","author":"O Rudolph","year":"2005","unstructured":"Rudolph, O.: Further results on the cross norm criterion for separability. Quantum Inf. Process. 4, 219\u2013239 (2005)","journal-title":"Quantum Inf. Process."},{"key":"1862_CR7","first-page":"193","volume":"3","author":"K Chen","year":"2003","unstructured":"Chen, K., Ling-An, W.: A matrix realignment method for recognizing entanglement. Quantum Inf. Comput. 3, 193\u2013202 (2003)","journal-title":"Quantum Inf. Comput."},{"key":"1862_CR8","first-page":"624","volume":"7","author":"JI Vicente de","year":"2007","unstructured":"de Vicente, J.I.: Separability criteria based on the Bloch representation of density matrices. Quantum Inf. Comput. 7, 624\u2013638 (2007)","journal-title":"Quantum Inf. Comput."},{"key":"1862_CR9","doi-asserted-by":"publisher","first-page":"022325","DOI":"10.1103\/PhysRevA.89.022325","volume":"89","author":"M Li","year":"2014","unstructured":"Li, M., Wang, J., Fei, S.-M., Li-Jost, X.: Quantum separability criteria for arbitrary-dimensional multipartite states. Phys. Rev. A 89, 022325 (2014)","journal-title":"Phys. Rev. A"},{"key":"1862_CR10","doi-asserted-by":"publisher","first-page":"032103","DOI":"10.1103\/PhysRevA.68.032103","volume":"68","author":"HF Hofmann","year":"2003","unstructured":"Hofmann, H.F., Takeuchi, S.: Violation of local uncertainty relations as a signature of entanglement. Phys. Rev. A 68, 032103 (2003)","journal-title":"Phys. Rev. A"},{"key":"1862_CR11","doi-asserted-by":"publisher","first-page":"022318","DOI":"10.1103\/PhysRevA.79.022318","volume":"79","author":"J Sperling","year":"2009","unstructured":"Sperling, J., Vogel, W.: Necessary and sufficient conditions for bipartite entanglement. Phys. Rev. A 79, 022318 (2009)","journal-title":"Phys. Rev. A"},{"key":"1862_CR12","doi-asserted-by":"publisher","first-page":"012324","DOI":"10.1103\/PhysRevA.81.012324","volume":"81","author":"C-J Zhang","year":"2010","unstructured":"Zhang, C.-J., Nha, H., Zhang, Y.-S., Guo, G.-C.: Entanglement detection via tighter local uncertainty relations. Phys. Rev. A 81, 012324 (2010)","journal-title":"Phys. Rev. A"},{"key":"1862_CR13","doi-asserted-by":"publisher","first-page":"130504","DOI":"10.1103\/PhysRevLett.99.130504","volume":"99","author":"O G\u00fchne","year":"2007","unstructured":"G\u00fchne, O., Hyllus, P., Gittsovich, O., Eisert, J.: Covariance matrices and the separability problem. Phys. Rev. Lett. 99, 130504 (2007)","journal-title":"Phys. Rev. Lett."},{"key":"1862_CR14","doi-asserted-by":"publisher","first-page":"032333","DOI":"10.1103\/PhysRevA.81.032333","volume":"81","author":"O Gittsovich","year":"2010","unstructured":"Gittsovich, O., G\u00fchne, O.: Quantifying entanglement with covariance matrices. Phys. Rev. A 81, 032333 (2010)","journal-title":"Phys. Rev. A"},{"key":"1862_CR15","doi-asserted-by":"publisher","first-page":"1442","DOI":"10.1038\/s41598-018-19709-z","volume":"8","author":"J-L Li","year":"2018","unstructured":"Li, J.-L., Qiao, C.-F.: A necessary and sufficient criterion for the separability of quantum state. Sci. Rep. 8, 1442 (2018)","journal-title":"Sci. Rep."},{"key":"1862_CR16","volume-title":"Matrix Analysis","author":"RA Horn","year":"2013","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis, 2nd edn. Cambridge University Press, Cambridge (2013)","edition":"2"},{"key":"1862_CR17","doi-asserted-by":"publisher","first-page":"012103","DOI":"10.1103\/PhysRevA.68.012103","volume":"68","author":"F Verstraete","year":"2003","unstructured":"Verstraete, F., Dehaene, J., De Moor, B.: Normal forms and entanglement measures for multipartite quantum state. Phys. Rev. A 68, 012103 (2003)","journal-title":"Phys. Rev. A"},{"key":"1862_CR18","doi-asserted-by":"publisher","first-page":"325301","DOI":"10.1088\/1751-8121\/aa7a2d","volume":"50","author":"SM Zangi","year":"2017","unstructured":"Zangi, S.M., Li, J.-L., Qiao, C.-F.: Entanglement classification of four-partite states under the SLOCC. J. Phys. A Math. Theor. 50, 325301 (2017)","journal-title":"J. Phys. A Math. Theor."},{"key":"1862_CR19","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/S0377-0427(00)00393-9","volume":"123","author":"CF Loan Van","year":"2000","unstructured":"Van Loan, C.F.: The ubiquitous Kronecker product. J. Comput. Appl. Math. 123, 85\u2013100 (2000)","journal-title":"J. Comput. Appl. Math."},{"key":"1862_CR20","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in Matrix Analysis","author":"RA Horn","year":"1991","unstructured":"Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Cambridge University Press, Cambridge (1991)"},{"key":"1862_CR21","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-68276-1","volume-title":"Inequalities: Theory of Majorization and Its Applications","author":"AW Marshall","year":"2011","unstructured":"Marshall, A.W., Olkin, I., Arnold, B.C.: Inequalities: Theory of Majorization and Its Applications, 2nd edn. Springer, Berlin (2011)","edition":"2"},{"key":"1862_CR22","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/S0375-9601(03)00941-1","volume":"314","author":"G Kimura","year":"2003","unstructured":"Kimura, G.: The Bloch vector for \n                    \n                      \n                    \n                    $$N$$\n                    \n                      \n                        N\n                      \n                    \n                  -level systems. Phys. Lett. A 314, 339\u2013349 (2003)","journal-title":"Phys. Lett. A"},{"key":"1862_CR23","doi-asserted-by":"publisher","first-page":"042315","DOI":"10.1103\/PhysRevA.64.042315","volume":"64","author":"P Rungta","year":"2001","unstructured":"Rungta, P., Bu\u017eek, V., Caves, C.M., Hillery, M., Milburn, G.J.: Universal state inversion and concurrence in arbitrary dimensions. Phys. Rev. A 64, 042315 (2001)","journal-title":"Phys. Rev. A"},{"key":"1862_CR24","doi-asserted-by":"publisher","first-page":"020402","DOI":"10.1103\/PhysRevLett.113.020402","volume":"113","author":"S Jevtic","year":"2014","unstructured":"Jevtic, S., Pusey, M., Jennings, D., Rudolph, T.: Quantum steering ellipsoids. Phys. Rev. Lett. 113, 020402 (2014)","journal-title":"Phys. Rev. Lett."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-018-1862-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-018-1862-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-018-1862-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,1]],"date-time":"2019-03-01T19:33:08Z","timestamp":1551468788000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-018-1862-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,2]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["1862"],"URL":"https:\/\/doi.org\/10.1007\/s11128-018-1862-5","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,2]]},"assertion":[{"value":"28 September 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 February 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"92"}}