{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T17:10:05Z","timestamp":1748884205802,"version":"3.41.0"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T00:00:00Z","timestamp":1747094400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["12075159","12075159"],"award-info":[{"award-number":["12075159","12075159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"the specific research fund of the Innovation Platform for Academicians of Hainan Province"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04758-x","type":"journal-article","created":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T07:55:38Z","timestamp":1747122938000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Realignment-based separability criteria and lower bounds of entanglement"],"prefix":"10.1007","volume":"24","author":[{"given":"Yu","family":"Lu","sequence":"first","affiliation":[]},{"given":"Zhong-Xi","family":"Shen","sequence":"additional","affiliation":[]},{"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[]},{"given":"Zhi-Xi","family":"Wang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,5,13]]},"reference":[{"key":"4758_CR1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.92.167902","volume":"92","author":"F Mintert","year":"2004","unstructured":"Mintert, F., Ku\u015b, M., Buchleitner, A.: Concurrence of mixed bipartite quantum states in arbitrary dimensions. Phys. Rev. Lett. 92, 167902 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"4758_CR2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.95.040504","volume":"95","author":"K Chen","year":"2005","unstructured":"Chen, K., Albeverio, S., Fei, S.M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95, 040504 (2005)","journal-title":"Phys. Rev. Lett."},{"key":"4758_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.97.080501","volume":"97","author":"HP Breuer","year":"2006","unstructured":"Breuer, H.P.: Optimal entanglement criterion for mixed quantum states. Phys. Rev. Lett. 97, 080501 (2006)","journal-title":"Phys. Rev. Lett."},{"key":"4758_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.75.052320","volume":"75","author":"JI de Vicente","year":"2007","unstructured":"de Vicente, J.I.: Lower bounds on concurrence and separability conditions. Phys. Rev. A 75, 052320 (2007)","journal-title":"Phys. Rev. A"},{"key":"4758_CR5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.012334","volume":"76","author":"CJ Zhang","year":"2007","unstructured":"Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Optimal entanglement witnesses based on local orthogonal observables. Phys. Rev. A 76, 012334 (2007)","journal-title":"Phys. Rev. A"},{"key":"4758_CR6","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":"4758_CR7","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 (1996)","journal-title":"Phys. Rev. Lett."},{"key":"4758_CR8","doi-asserted-by":"publisher","first-page":"865","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, 865 (1996)","journal-title":"Phys. Lett. A"},{"key":"4758_CR9","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/41\/41\/415301","volume":"41","author":"C Lupo","year":"2008","unstructured":"Lupo, C., Aniello, P., Scardicchio, A.: Bipartite quantum systems: on the realignment criterion and beyond. J. Phys. A: Math. Theor. 41, 415301 (2008)","journal-title":"J. Phys. A: Math. Theor."},{"key":"4758_CR10","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/44\/31\/315304","volume":"44","author":"CK Li","year":"2011","unstructured":"Li, C.K., Poon, Y.T., Sze, N.S.: A note on the realignment criterion. J. Phys. A: Math. Theor. 44, 315304 (2011)","journal-title":"J. Phys. A: Math. Theor."},{"key":"4758_CR11","doi-asserted-by":"publisher","first-page":"060301(R)","DOI":"10.1103\/PhysRevA.77.060301","volume":"77","author":"CJ Zhang","year":"2008","unstructured":"Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Entanglement detection beyond the computable cross-norm or realignment criterion. Phys. Rev. A 77, 060301(R) (2008)","journal-title":"Phys. Rev. A"},{"key":"4758_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.042332","volume":"92","author":"SQ Shen","year":"2015","unstructured":"Shen, S.Q., Wang, M.Y., Li, M., Fei, S.M.: Separability criteria based on the realignment of density matrices and reduced density matrices. Phys. Rev. A 92, 042332 (2015)","journal-title":"Phys. Rev. A"},{"key":"4758_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-017-1555-5","volume":"16","author":"YH Zhang","year":"2017","unstructured":"Zhang, Y.H., Lu, Y.Y., Wang, G.B., Shen, S.Q.: Realignment criteria for recognizing multipartite entanglement of quantum states. Quantum Inf. Process. 16, 1 (2017)","journal-title":"Quantum Inf. Process."},{"key":"4758_CR14","doi-asserted-by":"publisher","first-page":"17274","DOI":"10.1038\/s41598-017-17585-7","volume":"7","author":"M Li","year":"2017","unstructured":"Li, M., Wang, J., Shen, S.Q., Chen, Z.H., Fei, S.M.: Detection and measure of genuine tripartite entanglement with partial transposition and realignment of density matrices. Sci. Rep. 7, 17274 (2017)","journal-title":"Sci. Rep."},{"key":"4758_CR15","doi-asserted-by":"publisher","first-page":"131","DOI":"10.1007\/s11128-023-03875-9","volume":"22","author":"X Shi","year":"2023","unstructured":"Shi, X., Sun, Y.: A family of separability criteria and lower bounds of concurrence. Quantum Inf. Process. 22, 131 (2023)","journal-title":"Quantum Inf. Process."},{"key":"4758_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2024.107371","volume":"57","author":"XF Qi","year":"2024","unstructured":"Qi, X.F.: Detection and measure of genuine entanglement based on the realignment of density matrices for tripartite quantum states. Results Phys. 57, 107371 (2024)","journal-title":"Results Phys."},{"key":"4758_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.111.012415","volume":"111","author":"JX Sun","year":"2025","unstructured":"Sun, J.X., Yao, H.M., Fei, S.M., Fan, Z.B.: Separability and lower bounds of quantum entanglement based on realignment. Phys. Rev. A 111, 012415 (2025)","journal-title":"Phys. Rev. A"},{"key":"4758_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.physrep.2009.02.004","volume":"474","author":"O G\u00fchne","year":"2009","unstructured":"G\u00fchne, O., T\u00f3th, G.: Entanglement detection. Phys. Rep. 474, 1 (2009)","journal-title":"Phys. Rep."},{"key":"4758_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.68.062304","volume":"68","author":"S Lee","year":"2003","unstructured":"Lee, S., Chi, D.P., Oh, S.D., Kim, J.: Convex-roof extended negativity as an entanglement measure for bipartite quantum systems. Phys. Rev. A 68, 062304 (2003)","journal-title":"Phys. Rev. A"},{"key":"4758_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.042328","volume":"88","author":"M Huber","year":"2013","unstructured":"Huber, M., Perarnau-Llobet, M., de Vicente, J.I.: Entropy vector formalism and the structure of multidimensional entanglement in multipartite systems. Phys. Rev. A 88, 042328 (2013)","journal-title":"Phys. Rev. A"},{"key":"4758_CR21","doi-asserted-by":"publisher","first-page":"3761","DOI":"10.1007\/s11128-016-1369-x","volume":"15","author":"W Chen","year":"2016","unstructured":"Chen, W., Fei, S.M., Zheng, Z.J.: Lower bound on concurrence for arbitrary-dimensional tripartite quantum states. Quantum Inf. Process. 15, 3761\u20133771 (2016)","journal-title":"Quantum Inf. Process."},{"key":"4758_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.83.062325","volume":"83","author":"ZH Ma","year":"2011","unstructured":"Ma, Z.H., Chen, Z.H., Chen, J.L., Spengler, C., Gabriel, A., Huber, M.: Measure of genuine multipartite entanglement with computable lower bounds. Phys. Rev. A 83, 062325 (2011)","journal-title":"Phys. Rev. A"},{"key":"4758_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.96.052314","volume":"96","author":"M Li","year":"2017","unstructured":"Li, M., Jia, L.X., Wang, J., Shen, S.Q., Fei, S.M.: Measure and detection of genuine multipartite entanglement for tripartite systems. Phys. Rev. A 96, 052314 (2017)","journal-title":"Phys. Rev. A"},{"key":"4758_CR24","first-page":"193","volume":"3","author":"K Chen","year":"2003","unstructured":"Chen, K., Wu, L.A.: A matrix realignment method for recognizing entanglement. Quantum Inf. Comput. 3, 193 (2003)","journal-title":"Quantum Inf. Comput."},{"key":"4758_CR25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.77.060301","volume":"77","author":"CJ Zhang","year":"2008","unstructured":"Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Entanglement detection beyond the computable cross-norm or realignment criterion. Phys. Rev. A 77, 060301 (2008)","journal-title":"Phys. Rev. A"},{"key":"4758_CR26","doi-asserted-by":"publisher","first-page":"333","DOI":"10.1016\/S0375-9601(97)00416-7","volume":"232","author":"P Horodecki","year":"1997","unstructured":"Horodecki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232, 333 (1997)","journal-title":"Phys. Lett. A"},{"key":"4758_CR27","doi-asserted-by":"publisher","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":"4758_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.65.032314","volume":"65","author":"G Vidal","year":"2002","unstructured":"Vidal, G., Werner, R.F.: Computable measure of entanglement. Phys. Rev. A 65, 032314 (2002)","journal-title":"Phys. Rev. A"},{"key":"4758_CR29","doi-asserted-by":"publisher","first-page":"5385","DOI":"10.1103\/PhysRevLett.82.5385","volume":"82","author":"CH Bennett","year":"1999","unstructured":"Bennett, C.H., DiVincenzo, D.P., Mor, T., Shor, P.W., Smolin, J.A., Terhal, B.M.: Unextendible product bases and bound entanglement. Phys. Rev. Lett. 82, 5385 (1999)","journal-title":"Phys. Rev. Lett."},{"key":"4758_CR30","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/s10773-022-05253-0","volume":"61","author":"NH Jing","year":"2022","unstructured":"Jing, N.H., Zhang, M.M.: Criteria of genuine multipartite entanglement based on correlation tensors. Int. J. Theor. Phys. 61, 269 (2022)","journal-title":"Int. J. Theor. Phys."},{"key":"4758_CR31","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 (2005)","journal-title":"Quantum Inf. Process."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04758-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04758-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04758-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,2]],"date-time":"2025-06-02T16:39:44Z","timestamp":1748882384000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04758-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,5,13]]},"references-count":31,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["4758"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04758-x","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2025,5,13]]},"assertion":[{"value":"11 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 May 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"134"}}