{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T11:27:36Z","timestamp":1740137256950,"version":"3.37.3"},"reference-count":28,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2023,3,28]],"date-time":"2023-03-28T00:00:00Z","timestamp":1679961600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,3,28]],"date-time":"2023-03-28T00:00:00Z","timestamp":1679961600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["2008085MA20"],"award-info":[{"award-number":["2008085MA20"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"crossref","award":["2008085MA16"],"award-info":[{"award-number":["2008085MA16"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-023-03873-x","type":"journal-article","created":{"date-parts":[[2023,3,28]],"date-time":"2023-03-28T14:02:48Z","timestamp":1680012168000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Optimization of tripartite quantum steering inequalities via machine learning"],"prefix":"10.1007","volume":"22","author":[{"given":"Guo-Zhu","family":"Pan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4885-0755","authenticated-orcid":false,"given":"Ming","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming","family":"Kong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6534-2018","authenticated-orcid":false,"given":"Gang","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,28]]},"reference":[{"issue":"10","key":"3873_CR1","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 it quantum mechanical description of physical reality be considered complete? Phys. Rev. 47(10), 777 (1935)","journal-title":"Phys. Rev."},{"issue":"3","key":"3873_CR2","doi-asserted-by":"publisher","first-page":"446","DOI":"10.1017\/S0305004100019137","volume":"32","author":"E Schr\u00f6dinger","year":"1936","unstructured":"Schr\u00f6dinger, E.: Probability relations between separated systems. Proc. Camb. Philos. Soc. 32(3), 446 (1936)","journal-title":"Proc. Camb. Philos. Soc."},{"issue":"5","key":"3873_CR3","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.76.052116","volume":"76","author":"SJ Jones","year":"2007","unstructured":"Jones, S.J., Wiseman, H.M., Doherty, A.C.: Entanglement, Einstein\u2013Podolsky-Rosen correlations, Bell nonlocality, and steering. Phys. Rev. A 76(5), 052116 (2007)","journal-title":"Phys. Rev. A"},{"issue":"20","key":"3873_CR4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.200402","volume":"112","author":"J Bowles","year":"2014","unstructured":"Bowles, J., V\u00e9rtesi, T., Quintino, M.T., Brunner, N.: One-way Einstein\u2013Podolsky\u2013Rosen steering. Phys. Rev. Lett. 112(20), 200402 (2014)","journal-title":"Phys. Rev. Lett."},{"key":"3873_CR5","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1038\/nphoton.2012.202","volume":"6","author":"V H\u00e4ndchen","year":"2012","unstructured":"H\u00e4ndchen, V., Eberle, T., Steinlechner, S., Samblowski, A., Franz, T., Werner, R.F., Schnabel, R.: Observation of one-way Einstein\u2013Podolsky\u2013Rosen steering. Nat. Photonics 6, 596 (2012)","journal-title":"Nat. Photonics"},{"issue":"16","key":"3873_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.160403","volume":"116","author":"S Wollmann","year":"2016","unstructured":"Wollmann, S., Walk, N., Bennet, A.J., Wiseman, H.M., Pryde, G.J.: Observation of genuine one-way Einstein\u2013Podolsky\u2013Rosen steering. Phys. Rev. Lett. 116(16), 160403 (2016)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"3873_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.060404","volume":"114","author":"M Piani","year":"2015","unstructured":"Piani, M., Watrous, J.: Necessary and sufficient quantum information characterization of Einstein\u2013Podolsky\u2013Rosen steering. Phys. Rev. Lett. 114(6), 060404 (2015)","journal-title":"Phys. Rev. Lett."},{"key":"3873_CR8","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1038\/s41534-018-0067-1","volume":"4","author":"K Sun","year":"2018","unstructured":"Sun, K., Ye, X.J., Xiao, Y., Xu, X.Y., Wu, Y.C., Xu, J.S., Chen, J.L., Li, C.F., Guo, G.C.: Demonstration of Einstein CPodolsky CRosen steering with enhanced subchannel discrimination. NPJ Quantum Inf. 4, 12 (2018)","journal-title":"NPJ Quantum Inf."},{"issue":"6","key":"3873_CR9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.88.062338","volume":"88","author":"MD Reid","year":"2013","unstructured":"Reid, M.D.: Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities. Phys. Rev. A 88(6), 062338 (2013)","journal-title":"Phys. Rev. A"},{"issue":"18","key":"3873_CR10","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.115.180502","volume":"115","author":"Q He","year":"2015","unstructured":"He, Q., Rosales-Z\u00e1rate, L., Adesso, G., Reid, M.D.: Secure continuous variable teleportation and Einstein\u2013Podolsky\u2013Rosen steering. Phys. Rev. Lett. 115(18), 180502 (2015)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"3873_CR11","doi-asserted-by":"publisher","first-page":"634","DOI":"10.1364\/OPTICA.3.000634","volume":"3","author":"N Walk","year":"2016","unstructured":"Walk, N., Hosseini, S., Geng, J., Thearle, O., Haw, J.Y., Armstrong, S., Assad, S.M., Janousek, J., Ralph, T.C., Symul, T., Wiseman, H.M., Lam, P.K.: Experimental demonstration of Gaussian protocols for one-sided device-independent quantum key distribution. Optica 3(6), 634 (2016)","journal-title":"Optica"},{"issue":"1","key":"3873_CR12","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.012315","volume":"95","author":"I Kogias","year":"2017","unstructured":"Kogias, I., Xiang, Y., He, Q., Adesso, G.: Unconditional security of entanglement-based continuous-variable quantum secret sharing. Phys. Rev. A 95(1), 012315 (2017)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"3873_CR13","doi-asserted-by":"publisher","first-page":"010301(R)","DOI":"10.1103\/PhysRevA.85.010301","volume":"85","author":"C Branciard","year":"2012","unstructured":"Branciard, C., Cavalcanti, E.G., Walborn, S.P., Scarani, V., Wiseman, H.M.: One-sided device-independent quantum key distribution: security, feasibility, and the connection with steering. Phys. Rev. A 85(1), 010301(R) (2012)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"3873_CR14","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.052311","volume":"93","author":"C Jebaratnam","year":"2016","unstructured":"Jebaratnam, C.: Detecting genuine multipartite entanglement in steering scenarios. Phys. Rev. A 93(5), 052311 (2016)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"3873_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.80.032112","volume":"80","author":"EG Cavalcanti","year":"2009","unstructured":"Cavalcanti, E.G., Jones, S.J., Wiseman, H.M., Reid, M.D.: Experimental criteria for steering and the Einstein\u2013Podolsky\u2013Rosen paradox. Phys. Rev. A 80(3), 032112 (2009)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"3873_CR16","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.012142","volume":"95","author":"YL Zheng","year":"2017","unstructured":"Zheng, Y.L., Zhen, Y.Z., Chen, Z.B., Liu, N.L., Chen, K., Pan, J.W.: Efficient linear criterion for witnessing Einstein\u2013Podolsky\u2013Rosen nonlocality under many-setting local measurements. Phys. Rev. A 95(1), 012142 (2017)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"3873_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.95.032128","volume":"95","author":"YL Zheng","year":"2017","unstructured":"Zheng, Y.L., Zhen, Y.Z., Cao, W.F., Li, L., Chen, Z.B., Liu, N.L., Chen, K.: Optimized detection of steering via linear criteria for arbitrary-dimensional states. Phys. Rev. A 95(3), 032128 (2017)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"3873_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.87.062103","volume":"87","author":"J Schneeloch","year":"2013","unstructured":"Schneeloch, J., Broadbent, C.J., Walborn, S.P., Cavalcanti, E.G., Howell, J.C.: Einstein\u2013Podolsky\u2013Rosen steering inequalities from entropic uncertainty relations. Phys. Rev. A 87(6), 062103 (2013)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"3873_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.012108","volume":"93","author":"YZ Zhen","year":"2016","unstructured":"Zhen, Y.Z., Zheng, Y.L., Cao, W.F., Li, L., Chen, Z.B., Liu, N.L., Chen, K.: Certifying Einstein\u2013Podolsky\u2013Rosen steering via the local uncertainty principle. Phys. Rev. A 93(1), 012108 (2016)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"3873_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.062130","volume":"92","author":"SW Ji","year":"2015","unstructured":"Ji, S.W., Lee, J., Park, J., Nha, H.: Steering criteria via covariance matrices of local observables in arbitrary-dimensional quantum systems. Phys. Rev. A 92(6), 062130 (2015)","journal-title":"Phys. Rev. A"},{"key":"3873_CR21","doi-asserted-by":"publisher","first-page":"7941","DOI":"10.1038\/ncomms8941","volume":"6","author":"D Cavalcanti","year":"2015","unstructured":"Cavalcanti, D., Skrzypczyk, P., Aguilar, G.H., Nery, R.V., Ribeiro, P.S., Walborn, S.P.: Detection of entanglement in asymmetric quantum networks and multipartite quantum steering. Nat. Commun. 6, 7941 (2015)","journal-title":"Nat. Commun."},{"issue":"19","key":"3873_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.112.190501","volume":"112","author":"N Wiebe","year":"2014","unstructured":"Wiebe, N., Granade, C., Ferrie, C., Cory, D.G.: Hamiltonian learning and certification using quantum resources. Phys. Rev. Lett. 112(19), 190501 (2014)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"3873_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.090405","volume":"116","author":"M Krenn","year":"2016","unstructured":"Krenn, M., Malik, M., Fickler, R., Lapkiewicz, R., Zeilinger, A.: Automated search for new quantum experiments. Phys. Rev. Lett. 116(9), 090405 (2016)","journal-title":"Phys. Rev. Lett."},{"key":"3873_CR24","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1038\/nphys4037","volume":"13","author":"EPL van Nieuwenburg","year":"2017","unstructured":"van Nieuwenburg, E.P.L., Liu, Y.-H., Huber, S.D.: Learning phase transitions by confusion. Nat. Phys. 13, 435 (2017)","journal-title":"Nat. Phys."},{"issue":"24","key":"3873_CR25","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.120.240402","volume":"120","author":"DL Deng","year":"2018","unstructured":"Deng, D.L.: Machine learning detection of bell nonlocality in quantum many-body systems. Phys. Rev. Lett. 120(24), 240402 (2018)","journal-title":"Phys. Rev. Lett."},{"key":"3873_CR26","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1038\/s41534-018-0081-3","volume":"4","author":"YC Ma","year":"2018","unstructured":"Ma, Y.C., Yung, M.H.: Transforming Bell\u2019s inequalities into state classifiers with machine learning. NPJ Quantum Inf. 4, 34 (2018)","journal-title":"NPJ Quantum Inf."},{"issue":"19","key":"3873_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.123.190401","volume":"123","author":"M Yang","year":"2019","unstructured":"Yang, M., Ren, C.L., Ma, Y.C., Xiao, Y., Ye, X.J., Song, L.L., Xu, J.S., Yung, M.H., Li, C.F., Guo, G.C.: Experimental simultaneous learning of multiple nonclassical correlations. Phys. Rev. Lett. 123(19), 190401 (2019)","journal-title":"Phys. Rev. Lett."},{"issue":"20","key":"3873_CR28","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.200401","volume":"122","author":"A Canabarro","year":"2019","unstructured":"Canabarro, A., Brito, S., Chaves, R.: Machine learning nonlocal correlations. Phys. Rev. Lett. 122(20), 200401 (2019)","journal-title":"Phys. Rev. Lett."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-023-03873-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-023-03873-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-023-03873-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,4]],"date-time":"2023-05-04T16:40:07Z","timestamp":1683218407000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-023-03873-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,3,28]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2023,4]]}},"alternative-id":["3873"],"URL":"https:\/\/doi.org\/10.1007\/s11128-023-03873-x","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2023,3,28]]},"assertion":[{"value":"28 February 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 February 2023","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2023","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"162"}}