{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T15:47:25Z","timestamp":1786981645776,"version":"3.56.0"},"reference-count":57,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2019,1,25]],"date-time":"2019-01-25T00:00:00Z","timestamp":1548374400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61601002"],"award-info":[{"award-number":["61601002"]}],"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":["11575001"],"award-info":[{"award-number":["11575001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012432","name":"CAS Key Laboratory of Quantum Information","doi-asserted-by":"crossref","award":["KQI201701"],"award-info":[{"award-number":["KQI201701"]}],"id":[{"id":"10.13039\/501100012432","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s11128-019-2196-7","type":"journal-article","created":{"date-parts":[[2019,1,25]],"date-time":"2019-01-25T08:15:38Z","timestamp":1548404138000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Entropic uncertainty relations in the spin-1 Heisenberg model"],"prefix":"10.1007","volume":"18","author":[{"given":"Wei-Nan","family":"Shi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fei","family":"Ming","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0545-6205","authenticated-orcid":false,"given":"Dong","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liu","family":"Ye","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,1,25]]},"reference":[{"key":"2196_CR1","doi-asserted-by":"publisher","first-page":"172","DOI":"10.1007\/BF01397280","volume":"43","author":"W Heisenberg","year":"1927","unstructured":"Heisenberg, W.: \u00dcber den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Z. Phys. 43, 172 (1927)","journal-title":"Z. Phys."},{"key":"2196_CR2","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1103\/PhysRev.34.163","volume":"34","author":"HP Robertson","year":"1929","unstructured":"Robertson, H.P.: Violation of Heisenberg\u2019s uncertainty principle. Phys. Rev. 34, 163 (1929)","journal-title":"Phys. Rev."},{"key":"2196_CR3","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/BF01391200","volume":"44","author":"EH Kennard","year":"1927","unstructured":"Kennard, E.H.: Zur Quantenmechanik einfacher Bewegungstypen. Z. Phys. 44, 326 (1927)","journal-title":"Z. Phys."},{"key":"2196_CR4","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1103\/PhysRevLett.50.631","volume":"50","author":"D Deutsch","year":"1983","unstructured":"Deutsch, D.: Uncertainty in quantum measurements. Phys. Rev. Lett. 50, 631 (1983)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR5","doi-asserted-by":"publisher","first-page":"3070","DOI":"10.1103\/PhysRevD.35.3070","volume":"35","author":"K Kraus","year":"1987","unstructured":"Kraus, K.: Complementary observables and uncertainty relations. Phys. Rev. D 35, 3070 (1987)","journal-title":"Phys. Rev. D"},{"key":"2196_CR6","doi-asserted-by":"publisher","first-page":"1103","DOI":"10.1103\/PhysRevLett.60.1103","volume":"60","author":"H Maassen","year":"1988","unstructured":"Maassen, H., Uffink, J.B.M.: Generalized entropic uncertainty relations. Phys. Rev. Lett. 60, 1103 (1988)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR7","doi-asserted-by":"publisher","first-page":"835","DOI":"10.1002\/andp.201600130","volume":"528","author":"AE Rastegin","year":"2016","unstructured":"Rastegin, A.E.: Entropic uncertainty relations for successive measurements of canonically conjugate observables. Ann. Phys. (Berlin) 528, 835\u2013844 (2016)","journal-title":"Ann. Phys. (Berlin)"},{"key":"2196_CR8","doi-asserted-by":"publisher","first-page":"020402","DOI":"10.1103\/PhysRevLett.103.020402","volume":"103","author":"JM Renes","year":"2009","unstructured":"Renes, J.M., Boileau, J.C.: Conjectured strong complementary information tradeoff. Phys. Rev. Lett. 103, 020402 (2009)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR9","doi-asserted-by":"publisher","first-page":"659","DOI":"10.1038\/nphys1734","volume":"6","author":"M Berta","year":"2010","unstructured":"Berta, M., Christandl, M., Colbeck, R., Renes, J.M., Renner, R.: The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659 (2010)","journal-title":"Nat. Phys."},{"key":"2196_CR10","doi-asserted-by":"publisher","first-page":"757","DOI":"10.1038\/nphys2048","volume":"7","author":"R Prevedel","year":"2011","unstructured":"Prevedel, R., Hamel, D.R., Colbeck, R., Fisher, K., Resch, K.J.: Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nat. Phys. 7, 757 (2011)","journal-title":"Nat. Phys."},{"key":"2196_CR11","doi-asserted-by":"publisher","first-page":"752","DOI":"10.1038\/nphys2047","volume":"7","author":"CF Li","year":"2011","unstructured":"Li, C.F., Xu, J.S., Xu, X.Y., Li, K., Guo, G.C.: Experimental investigation of the entanglement-assisted entropic uncertainty principle. Nat. Phys. 7, 752 (2011)","journal-title":"Nat. Phys."},{"key":"2196_CR12","volume-title":"Quantum Computation and Quantum Information","author":"MA Nielson","year":"2002","unstructured":"Nielson, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2002)"},{"key":"2196_CR13","doi-asserted-by":"publisher","first-page":"110506","DOI":"10.1103\/PhysRevLett.106.110506","volume":"106","author":"M Tomamichel","year":"2011","unstructured":"Tomamichel, M., Renner, R.: Uncertainty relation for smooth entropies. Phys. Rev. Lett. 106, 110506 (2011)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR14","doi-asserted-by":"publisher","first-page":"210405","DOI":"10.1103\/PhysRevLett.108.210405","volume":"108","author":"PJ Coles","year":"2012","unstructured":"Coles, P.J., Colbeck, R., Yu, Y., Zwolak, M.: Uncertainty relations from simple entropic properties. Phys. Rev. Lett. 108, 210405 (2012)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR15","doi-asserted-by":"publisher","first-page":"2239","DOI":"10.1007\/s11128-015-0950-z","volume":"14","author":"J Zhang","year":"2015","unstructured":"Zhang, J., Zhang, Y., Yu, C.S.: R\u00e9nyi entropy uncertainty relation for successive projective measurements. Quantum Inf. Process. 14, 2239 (2015)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR16","doi-asserted-by":"crossref","unstructured":"Pati, A.K., Wilde, M.M., Devi, A.R.U., Rajagopal, A.K., Sudha: Quantum discord and classical correlation can tighten the uncertainty principle in the presence of quantum memory. Phys. Rev. A 86, 042105 (2012)","DOI":"10.1103\/PhysRevA.86.042105"},{"key":"2196_CR17","doi-asserted-by":"publisher","first-page":"022112","DOI":"10.1103\/PhysRevA.89.022112","volume":"89","author":"PJ Coles","year":"2014","unstructured":"Coles, P.J., Piani, M.: Improved entropic uncertainty relations and information exclusion relations. Phys. Rev. A 89, 022112 (2014)","journal-title":"Phys. Rev. A"},{"key":"2196_CR18","doi-asserted-by":"publisher","first-page":"062123","DOI":"10.1103\/PhysRevA.93.062123","volume":"93","author":"F Adabi","year":"2016","unstructured":"Adabi, F., Salimi, S., Haseli, S.: Tightening the entropic uncertainty bound in the presence of quantum memory. Phys. Rev. A 93, 062123 (2016)","journal-title":"Phys. Rev. A"},{"key":"2196_CR19","doi-asserted-by":"publisher","first-page":"981","DOI":"10.1007\/s11128-015-1187-6","volume":"15","author":"T Pramanik","year":"2016","unstructured":"Pramanik, T., Mal, S., Majumdar, A.S.: Lower bound of quantum uncertainty from extractable classical information. Quantum Inf. Process. 15, 981\u2013999 (2016)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR20","doi-asserted-by":"publisher","first-page":"032338","DOI":"10.1103\/PhysRevA.86.032338","volume":"86","author":"ML Hu","year":"2012","unstructured":"Hu, M.L., Fan, H.: Quantum-memory-assisted entropic uncertainty principle, teleportation, and entanglement witness in structured reservoirs. Phys. Rev. A 86, 032338 (2012)","journal-title":"Phys. Rev. A"},{"key":"2196_CR21","doi-asserted-by":"publisher","first-page":"022314","DOI":"10.1103\/PhysRevA.87.022314","volume":"87","author":"ML Hu","year":"2013","unstructured":"Hu, M.L., Fan, H.: Competitions between quantum correlations in the quantum-memory-assisted entropic uncertainty relation. Phys. Rev. A 87, 022314 (2013)","journal-title":"Phys. Rev. A"},{"key":"2196_CR22","doi-asserted-by":"publisher","first-page":"014105","DOI":"10.1103\/PhysRevA.88.014105","volume":"88","author":"ML Hu","year":"2013","unstructured":"Hu, M.L., Fan, H.: Upper bound and shareability of quantum discord based on entropic uncertainty relations. Phys. Rev. A 88, 014105 (2013)","journal-title":"Phys. Rev. A"},{"key":"2196_CR23","doi-asserted-by":"publisher","first-page":"11701","DOI":"10.1038\/srep11701","volume":"5","author":"J Zhang","year":"2015","unstructured":"Zhang, J., Zhang, Y., Yu, C.S.: Entropic uncertainty relation and information exclusion relation for multiple measurements in the presence of quantum memory. Sci. Rep. 5, 11701 (2015)","journal-title":"Sci. Rep."},{"key":"2196_CR24","doi-asserted-by":"publisher","first-page":"042133","DOI":"10.1103\/PhysRevA.91.042133","volume":"91","author":"S Liu","year":"2015","unstructured":"Liu, S., Mu, L.Z., Fan, H.: Entropic uncertainty relations for multiple measurements. Phys. Rev. A 91, 042133 (2015)","journal-title":"Phys. Rev. A"},{"key":"2196_CR25","doi-asserted-by":"publisher","first-page":"60004","DOI":"10.1209\/0295-5075\/115\/60004","volume":"115","author":"F Adabi","year":"2016","unstructured":"Adabi, F., Haseli, S., Salimi, S.: Reducing the entropic uncertainty lower bound in the presence of quantum memory via LOCC. EPL 115, 60004 (2016)","journal-title":"EPL"},{"key":"2196_CR26","doi-asserted-by":"publisher","first-page":"355301","DOI":"10.1088\/1751-8113\/49\/35\/355301","volume":"49","author":"AE Rastegin","year":"2016","unstructured":"Rastegin, A.E., Zyczkowski, K.: Majorization entropic uncertainty relations for quantum operations. J. Phys. A Math. Theor. 49, 355301 (2016)","journal-title":"J. Phys. A Math. Theor."},{"key":"2196_CR27","doi-asserted-by":"publisher","first-page":"1066","DOI":"10.1038\/s41598-017-01094-8","volume":"7","author":"D Wang","year":"2017","unstructured":"Wang, D., Huang, A.J., Ming, F., Sun, W.Y., Shi, J.D., Ye, L.: Entropic uncertainty relations for Markovian and non-Markovian processes under a structured bosonic reservoir. Sci. Rep. 7, 1066 (2017)","journal-title":"Sci. Rep."},{"key":"2196_CR28","doi-asserted-by":"publisher","first-page":"30228","DOI":"10.1038\/srep30228","volume":"6","author":"K Baek","year":"2016","unstructured":"Baek, K., Son, W.: Unsharpness of generalized measurement and its effects in entropic uncertainty relations. Sci. Rep. 6, 30228 (2016)","journal-title":"Sci. Rep."},{"key":"2196_CR29","doi-asserted-by":"publisher","first-page":"073004","DOI":"10.1088\/1367-2630\/18\/7\/073004","volume":"18","author":"M Berta","year":"2016","unstructured":"Berta, M., Wehner, S., Wilde, M.M.: Entropic uncertainty and measurement reversibility. New J. Phys. 18, 073004 (2016)","journal-title":"New J. Phys."},{"key":"2196_CR30","doi-asserted-by":"publisher","first-page":"055205","DOI":"10.1088\/1612-202X\/aa66fc","volume":"14","author":"D Wang","year":"2017","unstructured":"Wang, D., Ming, F., Huang, A.J., Sun, W.Y., Shi, J.D., Ye, L.: Exploration of quantum-memory-assisted entropic uncertainty relations in a noninertial frame. Laser Phys. Lett. 14, 055205 (2017)","journal-title":"Laser Phys. Lett."},{"key":"2196_CR31","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1007\/s11128-016-1503-9","volume":"16","author":"AJ Huang","year":"2017","unstructured":"Huang, A.J., Shi, J.D., Wang, D., Ye, L.: Steering quantum-memory-assisted entropic uncertainty under unital and nonunital noises via filtering operations. Quantum Inf. Process. 16, 46 (2017)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR32","doi-asserted-by":"publisher","first-page":"1800080","DOI":"10.1002\/andp.201800080","volume":"530","author":"D Wang","year":"2018","unstructured":"Wang, D., Shi, W.N., Hoehn, R.D., Ming, F., Sun, W.Y., Kais, S., Ye, L.: Effects of Hawking radiation on the entropic uncertainty in a Schwarzschild space-time. Ann. Phys. (Berlin) 530, 1800080 (2018)","journal-title":"Ann. Phys. (Berlin)"},{"key":"2196_CR33","doi-asserted-by":"publisher","first-page":"012113","DOI":"10.1103\/PhysRevA.86.012113","volume":"86","author":"ZY Xu","year":"2012","unstructured":"Xu, Z.Y., Yang, W.L., Feng, M.: Quantum-memory-assisted entropic uncertainty relation under noise. Phys. Rev. A 86, 012113 (2012)","journal-title":"Phys. Rev. A"},{"key":"2196_CR34","doi-asserted-by":"publisher","first-page":"115101","DOI":"10.1088\/0031-8949\/89\/11\/115101","volume":"89","author":"HM Zou","year":"2014","unstructured":"Zou, H.M., Fang, M.F., Yang, B.Y., Guo, Y.N., He, W., Zhang, S.Y.: The quantum entropic uncertainty relation and entanglement witness in the two-atom system coupling with the non-Markovian environments. Phys. Scr. 89, 115101 (2014)","journal-title":"Phys. Scr."},{"key":"2196_CR35","doi-asserted-by":"publisher","first-page":"527","DOI":"10.1016\/j.physletb.2013.08.069","volume":"726","author":"J Feng","year":"2013","unstructured":"Feng, J., Zhang, Y.Z., Gould, M.D., Fan, H.: Entropic uncertainty relations under the relativistic motion. Phys. Lett. B 726, 527 (2013)","journal-title":"Phys. Lett. B"},{"key":"2196_CR36","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/j.aop.2014.10.019","volume":"353","author":"LJ Jia","year":"2015","unstructured":"Jia, L.J., Tian, Z.H., Jing, J.L.: Entropic uncertainty relation in de Sitter space. Ann. Phys. 353, 37 (2015)","journal-title":"Ann. Phys."},{"key":"2196_CR37","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/s11128-018-1822-0","volume":"17","author":"YL Zhang","year":"2018","unstructured":"Zhang, Y.L., Fang, M.F., Kang, G.D., Zhou, Q.P.: Controlling quantum memory-assisted entropic uncertainty in non-Markovian environments. Quantum Inf. Process. 17, 62 (2018)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR38","doi-asserted-by":"publisher","unstructured":"Zhang, Z.Y., Liu, J.M., Hu, Z.H., Wang, Y.Z.: Entropic uncertainty relation for Dirac particles in Garfinkle\u2013Horowitz\u2013Strominger dilation space-time. Ann. Phys. (Berlin). \n                    https:\/\/doi.org\/10.1002\/andp.201800208\n                    \n                   (2018)","DOI":"10.1002\/andp.201800208"},{"key":"2196_CR39","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s11128-018-1846-5","volume":"17","author":"ZM Huang","year":"2018","unstructured":"Huang, Z.M.: Dynamics of entropic uncertainty for atoms immersed in thermal fluctuating massless scalar field. Quantum Inf. Process. 17, 73 (2018)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR40","doi-asserted-by":"publisher","first-page":"1093","DOI":"10.1109\/TIT.2014.2371464","volume":"61","author":"F Dupuis","year":"2015","unstructured":"Dupuis, F., Fawzi, O., Wehner, S.: Entanglement sampling and applications. IEEE. Trans. Inf. Theory 61, 1093 (2015)","journal-title":"IEEE. Trans. Inf. Theory"},{"key":"2196_CR41","doi-asserted-by":"publisher","first-page":"1962","DOI":"10.1109\/TIT.2011.2177772","volume":"58","author":"R Koening","year":"2012","unstructured":"Koening, R., Wehner, S., Wullschleger, J.: Unconditional security from noisy quantum storage. IEEE. Trans. Inf. Theory 58, 1962\u20131984 (2012)","journal-title":"IEEE. Trans. Inf. Theory"},{"key":"2196_CR42","doi-asserted-by":"publisher","first-page":"127902","DOI":"10.1103\/PhysRevLett.88.127902","volume":"88","author":"NJ Cerf","year":"2002","unstructured":"Cerf, N.J., Bourennane, M., Karlsson, A., Gisin, N.: Security of quantum key distribution using d-level systems. Phys. Rev. Lett. 88, 127902 (2002)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR43","doi-asserted-by":"publisher","first-page":"047905","DOI":"10.1103\/PhysRevLett.92.047905","volume":"92","author":"F Grosshans","year":"2004","unstructured":"Grosshans, F., Cerf, N.J.: Continuous-variable quantum cryptography is secure against non-Gaussian attacks. Phys. Rev. Lett. 92, 047905 (2004)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR44","doi-asserted-by":"publisher","first-page":"052327","DOI":"10.1103\/PhysRevA.90.052327","volume":"90","author":"G Vallone","year":"2014","unstructured":"Vallone, G., Marangon, D.G., Tomasin, M., Villoresi, P.: Quantum randomness certified by the uncertainty principle. Phys. Rev. A 90, 052327 (2014)","journal-title":"Phys. Rev. A"},{"key":"2196_CR45","doi-asserted-by":"publisher","first-page":"013010","DOI":"10.1088\/1367-2630\/17\/1\/013010","volume":"17","author":"M Jarzyna","year":"2015","unstructured":"Jarzyna, M., Demkowicz-Dobrza\u0144ski, R.: True precision limits in quantum metrology. New J. Phys. 17, 013010 (2015)","journal-title":"New J. Phys."},{"key":"2196_CR46","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-016-1481-y","volume":"16","author":"X Zheng","year":"2017","unstructured":"Zheng, X., Zhang, G.F.: The effects of mixedness and entanglement on the properties of the entropic uncertainty in Heisenberg model with Dzyaloshinski\u2013Moriya interaction. Quantum Inf. Process. 16, 1 (2017)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR47","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1007\/s11128-017-1657-0","volume":"16","author":"AJ Huang","year":"2017","unstructured":"Huang, A.J., Wang, D., Shi, J.D., Sun, W.Y., Ye, L.: Exploring entropic uncertainty relation in the Heisenberg XX model with inhomogeneous magnetic field. Quantum Inf. Process. 16, 204 (2017)","journal-title":"Quantum Inf. Process."},{"key":"2196_CR48","doi-asserted-by":"publisher","first-page":"065203","DOI":"10.1088\/1612-202X\/aa6f85","volume":"14","author":"D Wang","year":"2017","unstructured":"Wang, D., Huang, A.J., Ming, F., Sun, W.Y., Lu, H.P., Liu, C.C., Ye, L.: Quantum-memory-assisted entropic uncertainty relation in a Heisenberg XYZ chain with an inhomogeneous magnetic field. Laser Phys. Lett. 14, 065203 (2017)","journal-title":"Laser Phys. Lett."},{"key":"2196_CR49","doi-asserted-by":"publisher","first-page":"065207","DOI":"10.1088\/1612-202X\/aabb36","volume":"15","author":"ZY Zhang","year":"2018","unstructured":"Zhang, Z.Y., Wei, D.X., Liu, J.M.: Entropic uncertainty relation of a two-qutrit Heisenberg spin model in nonuniform magnetic fields and its dynamics under intrinsic decoherence. Laser Phys. Lett. 15, 065207 (2018)","journal-title":"Laser Phys. Lett."},{"key":"2196_CR50","unstructured":"Arfken, G.B., Weber, H.J., Harris, F.E.: Mathematical Methods for Physicists (7th ed.). Academic Press, Cambridge. ISBN 978-0-12-384654-9 (2000)"},{"key":"2196_CR51","unstructured":"Cheng, T.P., Li, L.F.: Gauge Theory of Elementary Particle Physics. Oxford University Press, Oxford. ISBN 0-19-851961-3 (1983)"},{"key":"2196_CR52","doi-asserted-by":"publisher","first-page":"777","DOI":"10.1103\/PhysRev.47.777","volume":"47","author":"A Einstein","year":"1935","unstructured":"Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)","journal-title":"Phys. Rev."},{"key":"2196_CR53","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":"2196_CR54","doi-asserted-by":"publisher","first-page":"865","DOI":"10.1103\/RevModPhys.81.865","volume":"81","author":"R Horodecki","year":"2009","unstructured":"Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865 (2009)","journal-title":"Rev. Mod. Phys."},{"key":"2196_CR55","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)","journal-title":"Phys. Rev. Lett."},{"key":"2196_CR56","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)","journal-title":"Phys. Rev. A"},{"key":"2196_CR57","doi-asserted-by":"publisher","first-page":"032314","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"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11128-019-2196-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2196-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-019-2196-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T19:26:24Z","timestamp":1579893984000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11128-019-2196-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,25]]},"references-count":57,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["2196"],"URL":"https:\/\/doi.org\/10.1007\/s11128-019-2196-7","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,25]]},"assertion":[{"value":"22 September 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 January 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 January 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"70"}}