{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,6]],"date-time":"2025-04-06T04:03:12Z","timestamp":1743912192195,"version":"3.40.3"},"reference-count":39,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T00:00:00Z","timestamp":1740960000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T00:00:00Z","timestamp":1740960000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"Research Award Fund for Natural Science Foundation of Shandong Province","award":["No. ZR2024MA068"],"award-info":[{"award-number":["No. ZR2024MA068"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04692-y","type":"journal-article","created":{"date-parts":[[2025,3,3]],"date-time":"2025-03-03T14:54:12Z","timestamp":1741013652000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Parameterized entanglement measures with computable lower bounds"],"prefix":"10.1007","volume":"24","author":[{"given":"Gui","family":"Bao","sequence":"first","affiliation":[]},{"given":"Xue-Na","family":"Zhu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,3,3]]},"reference":[{"key":"4692_CR1","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.65.042302","volume":"65","author":"J Barrett","year":"2002","unstructured":"Barrett, J.: Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality. Phys. Rev. A 65, 042302 (2002)","journal-title":"Phys. Rev. A"},{"key":"4692_CR2","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1103\/PhysRevA.56.1201","volume":"56","author":"R Cleve","year":"1997","unstructured":"Cleve, R., Buhrman, H.: Substituting quantum entanglement for communication. Phys. Rev. A 56, 1201 (1997)","journal-title":"Phys. Rev. A"},{"key":"4692_CR3","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.95.062320","volume":"95","author":"N Gigena","year":"2017","unstructured":"Gigena, N., Rossignoli, R.: Bipartite entanglement in fermion systems. Phys. Rev. A 95, 062320 (2017)","journal-title":"Phys. Rev. A"},{"key":"4692_CR4","doi-asserted-by":"crossref","first-page":"1769","DOI":"10.1098\/rsta.1998.0248","volume":"356","author":"A Ekert","year":"1998","unstructured":"Ekert, A., Jozsa, R.: Quantum algorithms: entanglementenhanced information processing. Philos. Trans. R. Soc. A 356, 1769 (1998)","journal-title":"Philos. Trans. R. Soc. A"},{"key":"4692_CR5","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":"4692_CR6","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.72.042316","volume":"72","author":"A Datta","year":"2005","unstructured":"Datta, A., Flammia, S.T., Caves, C.M.: Entanglement and the power of one qubit. Phys. Rev. A 72, 042316 (2005)","journal-title":"Phys. Rev. A"},{"key":"4692_CR7","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.64.042315","volume":"64","author":"P Rungta","year":"2001","unstructured":"Rungta, P., Buzek, 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":"4692_CR8","doi-asserted-by":"crossref","first-page":"2245","DOI":"10.1103\/PhysRevLett.80.2245","volume":"80","author":"WK Wootters","year":"1998","unstructured":"Wootters, W.K.: Entanglement of Formation of an Arbitrary State of Two Qubits. Phys. Rev. Lett. 80, 2245 (1998)","journal-title":"Phys. Rev. Lett."},{"key":"4692_CR9","doi-asserted-by":"crossref","first-page":"3824","DOI":"10.1103\/PhysRevA.54.3824","volume":"54","author":"CH Bennett","year":"1996","unstructured":"Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)","journal-title":"Phys. Rev. A"},{"key":"4692_CR10","first-page":"3","volume":"1","author":"M Horodecki","year":"2001","unstructured":"Horodecki, M.: Entanglement measures. Quantum Info. Comput. 1, 3 (2001)","journal-title":"Quantum Info. Comput."},{"key":"4692_CR11","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1103\/PhysRevA.58.883","volume":"58","author":"K Zyczkowski","year":"1998","unstructured":"Zyczkowski, K., Horodecki, P., Sanpera, A., Lewenstein, M.: Volume of the set of separable states. Phys. Rev. A 58, 883 (1998)","journal-title":"Phys. Rev. A"},{"key":"4692_CR12","doi-asserted-by":"crossref","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":"4692_CR13","volume":"81","author":"JS Kim","year":"2010","unstructured":"Kim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev. A 81, 062328 (2010)","journal-title":"Phys. Rev. A"},{"key":"4692_CR14","doi-asserted-by":"crossref","DOI":"10.1063\/1.2435088","volume":"48","author":"G Gour","year":"2007","unstructured":"Gour, G., Bandyopadhyay, S., Sanders, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48, 012108 (2007)","journal-title":"J. Math. Phys."},{"key":"4692_CR15","volume":"43","author":"JS Kim","year":"2010","unstructured":"Kim, J.S., Sanders, B.C.: Monogamy of multi-qubit entanglement using R$$\\acute{e}$$nyi entropy. J. Phys. A 43, 445305 (2010)","journal-title":"J. Phys. A"},{"key":"4692_CR16","doi-asserted-by":"crossref","unstructured":"Chen, K., Albeverio, S., Fei, S.M.: Entanglement of formation of bipartite quantum states. Phys. Rev. Lett. 95, 210501 (2005)","DOI":"10.1103\/PhysRevLett.95.210501"},{"key":"4692_CR17","volume":"95","author":"K Chen","year":"2005","unstructured":"Chen, K., Sergio, A., Fei, S.M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95, 040504 (2005)","journal-title":"Phys. Rev. Lett."},{"key":"4692_CR18","volume":"26","author":"LG Liu","year":"2009","unstructured":"Liu, L.G., Tian, C.L., Chen, P.X., Yuan, N.C.: A lower bound on concurrence. Chin. Phys. Lett. 26, 060306 (2009)","journal-title":"Chin. Phys. Lett."},{"key":"4692_CR19","doi-asserted-by":"crossref","first-page":"17274","DOI":"10.1038\/s41598-017-17585-7","volume":"7","author":"M Li","year":"2018","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 (2018)","journal-title":"Sci. Rep."},{"key":"4692_CR20","volume":"86","author":"XN Zhu","year":"2012","unstructured":"Zhu, X.N., Fei, S.M.: Improved lower and upper bounds for entanglement of formation. Phys. Rev. A 86, 054301 (2012)","journal-title":"Phys. Rev. A"},{"key":"4692_CR21","doi-asserted-by":"crossref","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":"4692_CR22","doi-asserted-by":"crossref","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 (1996)","journal-title":"Phys. Lett. A"},{"key":"4692_CR23","doi-asserted-by":"crossref","first-page":"4206","DOI":"10.1103\/PhysRevA.59.4206","volume":"59","author":"M Horodecki","year":"1999","unstructured":"Horodecki, M., Horodecki, P.: Reduction criterion of separability and limits for a class of distillation protocols. Phys. Rev. A 59, 4206 (1999)","journal-title":"Phys. Rev. A"},{"key":"4692_CR24","doi-asserted-by":"crossref","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."},{"key":"4692_CR25","first-page":"193","volume":"3","author":"K Chen","year":"2003","unstructured":"Chen, K., Wu, L.A.: A matrix realignment method for recognizing entanglement. Quantum Info. Comput. 3, 193 (2003)","journal-title":"Quantum Info. Comput."},{"key":"4692_CR26","volume":"103","author":"X Yang","year":"2021","unstructured":"Yang, X., Luo, M.X., Yang, Y.H., Fei, S.M.: Parametrized entanglement monotone. Phys. Rev. A 103, 052423 (2021)","journal-title":"Phys. Rev. A"},{"key":"4692_CR27","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1007\/s11128-022-03551-4","volume":"21","author":"ZW Wei","year":"2022","unstructured":"Wei, Z.W., Luo, M.X., Fei, S.M.: Estimating parameterized entanglement measure. Quantum Inform. Process. 21, 210 (2022)","journal-title":"Quantum Inform. Process."},{"issue":"27","key":"4692_CR28","volume":"55","author":"ZW Wei","year":"2022","unstructured":"Wei, Z.W., Fei, S.M.: Parameterized bipartite entanglement measure. J. Phys. A: Math. Theoretical 55(27), 275303 (2022)","journal-title":"J. Phys. A: Math. Theoretical"},{"key":"4692_CR29","doi-asserted-by":"crossref","first-page":"2300305","DOI":"10.1002\/andp.202300305","volume":"535","author":"X Shi","year":"2023","unstructured":"Shi, X., Chen, L.: A genuine multipartite entanglement measure generated by the parametrized entanglement measure. Annalen der Physik 535, 2300305 (2023)","journal-title":"Annalen der Physik"},{"key":"4692_CR30","volume":"4","author":"YF Li","year":"2022","unstructured":"Li, Y.F., Shang, J.W.: Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. Phys. Rev. Res. 4, 023059 (2022)","journal-title":"Phys. Rev. Res."},{"key":"4692_CR31","volume":"109","author":"H Li","year":"2024","unstructured":"Li, H., Gao, T., Yan, F.: Parametrized multipartite entanglement measures. Phys. Rev. A 109, 012213 (2024)","journal-title":"Phys. Rev. A"},{"key":"4692_CR32","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":"4692_CR33","doi-asserted-by":"crossref","first-page":"2275","DOI":"10.1103\/PhysRevLett.78.2275","volume":"78","author":"V Vedral","year":"1997","unstructured":"Vedral, V., Plenio, M.B., Rippin, M.A., Knight, P.L.: Quantifying entanglement. Phys. Rev. Lett. 78, 2275 (1997)","journal-title":"Phys. Rev. Lett."},{"key":"4692_CR34","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1103\/PhysRevA.57.1619","volume":"57","author":"V Vedral","year":"1998","unstructured":"Vedral, V., Plenio, M.B.: Entanglement measures and purification procedures. Phys. Rev. A. 57, 1619 (1998)","journal-title":"Phys. Rev. A."},{"key":"4692_CR35","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1103\/PhysRevA.59.141","volume":"59","author":"G Vidal","year":"1999","unstructured":"Vidal, G., Tarrach, R.: Robustness of entanglement. Phys. Rev. A. 59, 141 (1999)","journal-title":"Phys. Rev. A."},{"key":"4692_CR36","doi-asserted-by":"crossref","unstructured":"Mintert, F., Carvalho, A.R., Ku$$\\acute{s}$$, M., Buchleitner, A.: Measures and dynamics of entangled states. Phys. Rep. 415, 207 (2005)","DOI":"10.1016\/j.physrep.2005.04.006"},{"key":"4692_CR37","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.67.012307","volume":"67","author":"P Rungta","year":"2003","unstructured":"Rungta, P., Caves, C.M.: Concurrence-based entanglement measures for isotropic states. Phys. Rev. A 67, 012307 (2003)","journal-title":"Phys. Rev. A"},{"key":"4692_CR38","volume":"76","author":"G Gour","year":"2007","unstructured":"Gour, G.: Reexamination of entanglement of superpositions. Phys. Rev. A 76, 052320 (2007)","journal-title":"Phys. Rev. A"},{"key":"4692_CR39","volume":"103","author":"X Yang","year":"2021","unstructured":"Yang, X., Luo, M.X., Yang, Y.H., Fei, S.M.: Parametrized entanglement monotone. Phys. Rev. A 103, 052423 (2021)","journal-title":"Phys. Rev. A"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04692-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04692-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04692-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,4,5]],"date-time":"2025-04-05T03:41:58Z","timestamp":1743824518000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04692-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,3]]},"references-count":39,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["4692"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04692-y","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2025,3,3]]},"assertion":[{"value":"6 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 March 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 Conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"77"}}