{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T05:11:00Z","timestamp":1774501860170,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T00:00:00Z","timestamp":1721001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T00:00:00Z","timestamp":1721001600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"the Start-up Funding of Dongguan University of Technology","award":["No. 221110084"],"award-info":[{"award-number":["No. 221110084"]}]},{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["Grants 12075159, 12171044 and 12301582"],"award-info":[{"award-number":["Grants 12075159, 12171044 and 12301582"]}],"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\/s11128-024-04481-z","type":"journal-article","created":{"date-parts":[[2024,7,15]],"date-time":"2024-07-15T07:02:02Z","timestamp":1721026922000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Tighter monogamy relations of the $$S^{t}$$ and $$T^{t}_q$$-entropy entanglement measures based on dual entropy"],"prefix":"10.1007","volume":"23","author":[{"given":"Zhong-Xi","family":"Shen","sequence":"first","affiliation":[]},{"given":"Kang-Kang","family":"Yang","sequence":"additional","affiliation":[]},{"given":"Zhi-Xiang","family":"Jin","sequence":"additional","affiliation":[]},{"given":"Zhi-Xi","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Shao-Ming","family":"Fei","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,7,15]]},"reference":[{"key":"4481_CR1","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1088\/0253-6102\/67\/1\/27","volume":"67","author":"M Jafarpour","year":"2017","unstructured":"Jafarpour, M., Hasanvand, F.K., Afshar, D.: Dynamics of entanglement and measurement-induced disturbance for a hybrid qubit-qutrit system interacting with a spin-chain environment: a mean field approach. Commun. Theor. Phys. 67, 27 (2017). https:\/\/doi.org\/10.1088\/0253-6102\/67\/1\/27","journal-title":"Commun. Theor. Phys."},{"key":"4481_CR2","doi-asserted-by":"publisher","first-page":"60002","DOI":"10.1209\/0295-5075\/123\/60002","volume":"123","author":"MY Wang","year":"2018","unstructured":"Wang, M.Y., Xu, J.Z., Yan, F.L., Gao, T.: Entanglement concentration for polarization-spatial-time-bin hyperentangled Bell states. Europhys. Lett. 123, 60002 (2018). https:\/\/doi.org\/10.1209\/0295-5075\/123\/60002","journal-title":"Europhys. Lett."},{"key":"4481_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/s11433-018-9175-2","volume":"61","author":"HL Huang","year":"2018","unstructured":"Huang, H.L., Goswami, A.K., Bao, W.S., Panigrahi, P.K.: Demonstration of essentiality of entanglement in a Deutsch-like quantum algorithm. Sci. China-Phys. Mech. Astron. 61, 060311 (2018). https:\/\/doi.org\/10.1007\/s11433-018-9175-2","journal-title":"Sci. China-Phys. Mech. Astron."},{"key":"4481_CR4","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.scib.2016.11.007","volume":"62","author":"FG Deng","year":"2017","unstructured":"Deng, F.G., Ren, B.C., Li, X.H.: Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62, 46 (2017). https:\/\/doi.org\/10.1016\/j.scib.2016.11.007","journal-title":"Sci. Bull."},{"key":"4481_CR5","doi-asserted-by":"publisher","first-page":"5022","DOI":"10.1103\/PhysRevLett.78.5022","volume":"78","author":"S Hill","year":"1997","unstructured":"Hill, S., Wootters, W.K.: Entanglement of a pair of quantum bits. Phys. Rev. Lett. 78, 5022\u20135025 (1997). https:\/\/doi.org\/10.1103\/PhysRevLett.78.5022","journal-title":"Phys. Rev. Lett."},{"key":"4481_CR6","doi-asserted-by":"publisher","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). https:\/\/doi.org\/10.1103\/physreva.54.3824","journal-title":"Phys. Rev. A"},{"key":"4481_CR7","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/0375-9601(95)00930-2","volume":"210","author":"R Horodecki","year":"1996","unstructured":"Horodecki, R., Horodecki, P., Horodecki, M.: Quantum $$\\alpha $$-entropy inequalities: independent condition for local realism? Phys. Lett. A 210, 377\u2013381 (1996). https:\/\/doi.org\/10.1016\/0375-9601(95)00930-2","journal-title":"Phys. Lett. A"},{"key":"4481_CR8","doi-asserted-by":"publisher","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). https:\/\/doi.org\/10.1063\/1.2435088","journal-title":"J. Math. Phys."},{"key":"4481_CR9","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/43\/44\/445305","volume":"43","author":"JS Kim","year":"2010","unstructured":"Kim, J.S., Sanders, B.C.: Monogamy of multi-qubit entanglement using R\u00e9nyi entropy. J. Phys. A Math. Theor. 43, 445305 (2010). https:\/\/doi.org\/10.1088\/1751-8113\/43\/44\/445305","journal-title":"J. Phys. A Math. Theor."},{"key":"4481_CR10","doi-asserted-by":"publisher","first-page":"211","DOI":"10.1016\/S0375-9601(98)00500-3","volume":"247","author":"PT Landsberg","year":"1998","unstructured":"Landsberg, P.T., Vedral, V.: Distributions and channel capacities in generalized statistical mechanics. Phys. Lett. A 247, 211\u2013217 (1998). https:\/\/doi.org\/10.1016\/S0375-9601(98)00500-3","journal-title":"Phys. Lett. A"},{"key":"4481_CR11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.81.062328","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). https:\/\/doi.org\/10.1103\/PhysRevA.81.062328","journal-title":"Phys. Rev. A"},{"key":"4481_CR12","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/44\/29\/295303","volume":"44","author":"JS Kim","year":"2011","unstructured":"Kim, J.S., Sanders, B.C.: Unified entropy, entanglement measures and monogamy of multi-party entanglement. J. Phys. A Math. Theor. 44, 295303 (2011). https:\/\/doi.org\/10.1088\/1751-8113\/44\/29\/295303","journal-title":"J. Phys. A Math. Theor."},{"key":"4481_CR13","doi-asserted-by":"publisher","first-page":"654","DOI":"10.1140\/epjp\/s13360-023-04259-9","volume":"138","author":"X Yang","year":"2023","unstructured":"Yang, X., Yang, Y.H., Zhao, L.M., Luo, M.X.: A new entanglement measure based dual entropy. Eur. Phys. J. Plus 138, 654 (2023). https:\/\/doi.org\/10.1140\/epjp\/s13360-023-04259-9","journal-title":"Eur. Phys. J. Plus"},{"key":"4481_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.61.052306","volume":"138","author":"V Coffman","year":"2000","unstructured":"Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 138, 052306 (2000). https:\/\/doi.org\/10.1103\/PhysRevA.61.052306","journal-title":"Phys. Rev. A"},{"key":"4481_CR15","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1147\/rd.481.0071","volume":"48","author":"B Terhal","year":"2004","unstructured":"Terhal, B.: Is entanglement monogamous? IBM J. Res. Dev. 48, 71\u201378 (2004). https:\/\/doi.org\/10.1147\/rd.481.0071","journal-title":"IBM J. Res. Dev."},{"key":"4481_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.220503","volume":"96","author":"TJ Osborne","year":"2006","unstructured":"Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96, 220503 (2006). https:\/\/doi.org\/10.1103\/PhysRevLett.96.220503","journal-title":"Phys. Rev. Lett."},{"key":"4481_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/10.1103\/PhysRevA.89.034303","volume":"89","author":"TR de Oliveira","year":"2014","unstructured":"de Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89, 034303 (2014). https:\/\/doi.org\/10.1103\/10.1103\/PhysRevA.89.034303","journal-title":"Phys. Rev. A"},{"key":"4481_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.113.100503","volume":"113","author":"YK Bai","year":"2014","unstructured":"Bai, Y.K., Xu, Y.F., Wang, Z.D.: General monogamy relation for the entanglement of formation in multiqubit systems. Phys. Rev. Lett. 113, 100503 (2014). https:\/\/doi.org\/10.1103\/PhysRevLett.113.100503","journal-title":"Phys. Rev. Lett."},{"key":"4481_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/10.1103\/PhysRevA.90.062343","volume":"90","author":"YK Bai","year":"2014","unstructured":"Bai, Y.K., Xu, Y.F., Wang, Z.D.: Hierarchical monogamy relations for the squared entanglement of formation in multipartite systems. Phys. Rev. A 90, 062343 (2014). https:\/\/doi.org\/10.1103\/10.1103\/PhysRevA.90.062343","journal-title":"Phys. Rev. A"},{"key":"4481_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.022306","volume":"93","author":"W Song","year":"2016","unstructured":"Song, W., Bai, Y.K., Yang, M., Cao, Z.L.: General monogamy relation of multi-qubit system in terms of squared R\u00e9nyi-$$\\alpha $$ entanglement. Phys. Rev. A 93, 022306 (2016). https:\/\/doi.org\/10.1103\/PhysRevA.93.022306","journal-title":"Phys. Rev. A"},{"key":"4481_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/10.1103\/PhysRevA.93.062340","volume":"93","author":"Y Luo","year":"2016","unstructured":"Luo, Y., Tian, T., Shao, L.H., Li, Y.M.: General monogamy of Tsallis $$q$$-entropy entanglement in multiqubit systems, Phys. Rev. A 93, 062340 (2016). https:\/\/doi.org\/10.1103\/10.1103\/PhysRevA.93.062340","journal-title":"Rev. A"},{"key":"4481_CR22","doi-asserted-by":"publisher","first-page":"16419","DOI":"10.1038\/s41598-019-52817-y","volume":"9","author":"A Khan","year":"2019","unstructured":"Khan, A., ur Rehman, J., Wang, K., Shin, H.: Unified monogamy relations of multipartite entanglement. Sci. Rep. 9, 16419 (2019). https:\/\/doi.org\/10.1038\/s41598-019-52817-y","journal-title":"Sci. Rep."},{"key":"4481_CR23","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1063\/1.1643788","volume":"45","author":"M Christandl","year":"2004","unstructured":"Christandl, M., Winter, A.: \u201cSquashed entanglement\u2019\u2019: an additive entanglement measure. J. Math. Phys. 45, 829\u2013840 (2004). https:\/\/doi.org\/10.1063\/1.1643788","journal-title":"J. Math. Phys."},{"key":"4481_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.90.024304","volume":"90","author":"XN Zhu","year":"2014","unstructured":"Zhu, X.N., Fei, S.M.: Entanglement monogamy relations of qubit systems. Phys. Rev. A 90, 024304 (2014). https:\/\/doi.org\/10.1103\/PhysRevA.90.024304","journal-title":"Phys. Rev. A"},{"key":"4481_CR25","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.aop.2015.08.022","volume":"362","author":"Y Luo","year":"2015","unstructured":"Luo, Y., Li, Y.M.: Monogamy of $$\\alpha $$-th power entanglement measurement in qubit system. Ann. Phys. 362, 511\u2013520 (2015). https:\/\/doi.org\/10.1016\/j.aop.2015.08.022","journal-title":"Ann. Phys."},{"key":"4481_CR26","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s11128-017-1520-3","volume":"16","author":"ZX Jin","year":"2017","unstructured":"Jin, Z.X., Fei, S.M.: Tighter entanglement monogamy relations of qubit systems. Quantum Inf. Process. 16, 77 (2017). https:\/\/doi.org\/10.1007\/s11128-017-1520-3","journal-title":"Quantum Inf. Process."},{"key":"4481_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.97.032336","volume":"97","author":"ZX Jin","year":"2018","unstructured":"Jin, Z.X., Li, J., Li, T., Fei, S.M.: Tighter monogamy relations in multiqubit systems. Phys. Rev. A 97, 032336 (2018). https:\/\/doi.org\/10.1103\/PhysRevA.97.032336","journal-title":"Phys. Rev. A"},{"key":"4481_CR28","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.1126\/science.1232957","volume":"340","author":"M Walter","year":"2013","unstructured":"Walter, M., Doran, B., Gross, D., Christandl, M.: Entanglement polytopes: multiparticle entanglement from single-particle information. Science 340, 1205 (2013). https:\/\/doi.org\/10.1126\/science.1232957","journal-title":"Science"},{"key":"4481_CR29","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1007\/s11128-009-0161-6","volume":"9","author":"M P Seevinck","year":"2010","unstructured":"Seevinck, M. P.: Monogamy of correlations versus monogamy of entanglement. Quantum Inf. Process. 9, 273 (2010). https:\/\/doi.org\/10.1007\/s11128-009-0161-6","journal-title":"Quantum Inf. Process."},{"key":"4481_CR30","doi-asserted-by":"publisher","first-page":"399","DOI":"10.1038\/NPHYS1919","volume":"7","author":"XS Ma","year":"2011","unstructured":"Ma, X.S., Dakic, B., Naylor, W., Zeilinger, A., Walther, P.: Quantum simulation of the wavefunction to probe frustrated Heisenberg spin systems. Nat. Phys. 7, 399 (2011). https:\/\/doi.org\/10.1038\/NPHYS1919","journal-title":"Nat. Phys."},{"key":"4481_CR31","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1007\/JHEP10(2013)107","volume":"1310","author":"E Verlinde","year":"2013","unstructured":"Verlinde, E., Verlinde, H.: Black hole entanglement and quantum error correction. J. High Energy Phys. 1310, 107 (2013). https:\/\/doi.org\/10.1007\/JHEP10(2013)107","journal-title":"J. High Energy Phys."},{"key":"4481_CR32","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb00917.x","volume":"27","author":"CE Shannon","year":"1948","unstructured":"Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379\u2013423 (1948). https:\/\/doi.org\/10.1002\/j.1538-7305.1948.tb00917.x","journal-title":"Bell Syst. Tech. J."},{"key":"4481_CR33","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1214\/14-STS430","volume":"30","author":"F Lad","year":"2015","unstructured":"Lad, F., Sanfilippo, G., Agro, G.: Extropy: complementary dual of entropy. Stat. Sci. 30, 40\u201358 (2015). https:\/\/doi.org\/10.1214\/14-STS430","journal-title":"Stat. Sci."},{"key":"4481_CR34","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). https:\/\/doi.org\/10.1103\/PhysRevA.64.042315","journal-title":"Phys. Rev. A"},{"key":"4481_CR35","doi-asserted-by":"publisher","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). https:\/\/doi.org\/10.1103\/PhysRevLett.80.2245","journal-title":"Phys. Rev. Lett."},{"key":"4481_CR36","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/ab6720","volume":"29","author":"ZX Jin","year":"2020","unstructured":"Jin, Z.X., Qiao, C.F.: Monogamy and polygamy relations of multiqubit entanglement based on unified entropy. Chin. Phys. B 29, 020305 (2020). https:\/\/doi.org\/10.1088\/1674-1056\/ab6720","journal-title":"Chin. Phys. B"},{"issue":"5","key":"4481_CR37","doi-asserted-by":"publisher","first-page":"1159","DOI":"10.3390\/math11051159","volume":"11","author":"YH Tao","year":"2023","unstructured":"Tao, Y.H., Zheng, K., Jin, Z.X., Fei, S.M.: Tighter monogamy relations for concurrence and negativity in multiqubit systems. Mathematics 11(5), 1159 (2023). https:\/\/doi.org\/10.3390\/math11051159","journal-title":"Mathematics"},{"key":"4481_CR38","doi-asserted-by":"publisher","first-page":"1560","DOI":"10.1103\/PhysRevLett.85.1560","volume":"85","author":"A Acin","year":"2000","unstructured":"Acin, A., Andrianov, A., Costa, L., Jane, E., Latorre, J.I., Tarrach, R.: Generalized Schmidt decomposition and classification of three-quantum-bit states. Phys. Rev. Lett. 85, 1560 (2000). https:\/\/doi.org\/10.1103\/PhysRevLett.85.1560","journal-title":"Phys. Rev. Lett."},{"key":"4481_CR39","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1140\/epjst\/e2008-00694-x","volume":"159","author":"XH Gao","year":"2008","unstructured":"Gao, X.H., Fei, S.M.: Estimation of concurrence for multipartite mixed states. Eur. Phys. J. Spec. Top. 159, 71 (2008). https:\/\/doi.org\/10.1140\/epjst\/e2008-00694-x","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"4481_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.012327","volume":"93","author":"S Karmakar","year":"2016","unstructured":"Karmakar, S., Sen, A., Bhar, A., Sarkar, D.: Strong monogamy conjecture in a four-qubit system. Phys. Rev. A 93, 012327 (2016). https:\/\/doi.org\/10.1103\/PhysRevA.93.012327","journal-title":"Phys. Rev. A"},{"key":"4481_CR41","doi-asserted-by":"publisher","first-page":"28719","DOI":"10.1038\/srep28719","volume":"6","author":"GM Yuan","year":"2016","unstructured":"Yuan, G.M., Song, W., Yang, M., Li, D.C., Zhao, J.L., Cao, Z.L.: Monogamy relation of multi-qubit systems for squared Tsallis-q entanglement. Sci. Rep. 6, 28719 (2016). https:\/\/doi.org\/10.1038\/srep28719","journal-title":"Sci. Rep."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04481-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-024-04481-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-024-04481-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,30]],"date-time":"2024-07-30T17:40:49Z","timestamp":1722361249000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-024-04481-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,15]]},"references-count":41,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["4481"],"URL":"https:\/\/doi.org\/10.1007\/s11128-024-04481-z","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,7,15]]},"assertion":[{"value":"9 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 July 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 July 2024","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":"274"}}