{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,22]],"date-time":"2025-08-22T05:10:33Z","timestamp":1755839433483,"version":"3.37.3"},"reference-count":50,"publisher":"Springer Science and Business Media LLC","issue":"11","license":[{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T00:00:00Z","timestamp":1667260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61772437"],"award-info":[{"award-number":["61772437"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2682014CX095"],"award-info":[{"award-number":["2682014CX095"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-022-03713-4","type":"journal-article","created":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T18:03:00Z","timestamp":1667325780000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Detecting and embedding high-dimensional genuine multipartite entanglement states"],"prefix":"10.1007","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6558-1000","authenticated-orcid":false,"given":"Yan-Han","family":"Yang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xue","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ming-Xing","family":"Luo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,1]]},"reference":[{"key":"3713_CR1","doi-asserted-by":"crossref","unstructured":"Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)","DOI":"10.1103\/PhysRev.47.777"},{"key":"3713_CR2","doi-asserted-by":"crossref","unstructured":"Schr\u00f6dinger, E.: Die gegenw\u00e4rtige situation in der quantenmechanik. Naturwissenschaften 23, 807 (1935)","DOI":"10.1007\/BF01491891"},{"key":"3713_CR3","doi-asserted-by":"crossref","unstructured":"Bouwmeester, D., Zeilinger, A.: In: Bouwmeester, D., Ekert, A., Zeilinger, A. (eds.) The Physics of Quantum Information. Springer, Heidelberg (2000)","DOI":"10.1007\/978-3-662-04209-0"},{"key":"3713_CR4","doi-asserted-by":"crossref","unstructured":"Ekert, A.: Quantum cryptography based on Bell\u2019s theorem. Phys. Rev. Lett. 67, 661 (1991)","DOI":"10.1103\/PhysRevLett.67.661"},{"key":"3713_CR5","doi-asserted-by":"crossref","unstructured":"Bennett, C.H., Wiesner, S.J.: Communication via one- and two-particle operators on Einstein\u2013Podolsky\u2013Rosen states. Phys. Rev. Lett. 69, 2881 (1992)","DOI":"10.1103\/PhysRevLett.69.2881"},{"key":"3713_CR6","doi-asserted-by":"crossref","unstructured":"Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722 (1996)","DOI":"10.1103\/PhysRevLett.76.722"},{"key":"3713_CR7","doi-asserted-by":"crossref","unstructured":"Long, G.-L., Liu, X.-S.: Theoretically efficient high-capacity quantum-key distribution scheme. Phys. Rev. A 65, 032302 (2002)","DOI":"10.1103\/PhysRevA.65.032302"},{"key":"3713_CR8","doi-asserted-by":"crossref","unstructured":"Deng, F.-G., Long, G.-L., Liu, X.-S.: Two-step quantum direct communication protocol using the Einstein\u2013Podolsky\u2013Rosen pair block. Phys. Rev. A 68, 042317 (2003)","DOI":"10.1103\/PhysRevA.68.042317"},{"key":"3713_CR9","doi-asserted-by":"crossref","unstructured":"Sheng, Y.-B., Zhou, L., Long, G.-L.: One-step quantum secure direct communication. Sci. Bull. 67, 367 (2022)","DOI":"10.1016\/j.scib.2021.11.002"},{"key":"3713_CR10","doi-asserted-by":"crossref","unstructured":"Cerf, N.J., Massar, S., Pironio, S.: Greenberger\u2013Horne\u2013Zeilinger paradoxes for many qudits. Phys. Rev. Lett. 89, 080402 (2002)","DOI":"10.1103\/PhysRevLett.89.080402"},{"key":"3713_CR11","doi-asserted-by":"crossref","unstructured":"Lee, J., Lee, S.-W., Kim, M.S.: Greenberger\u2013Horne\u2013Zeilinger nonlocality in arbitrary even dimensions. Phys. Rev. A 73, 032316 (2006)","DOI":"10.1103\/PhysRevA.73.032316"},{"key":"3713_CR12","doi-asserted-by":"crossref","unstructured":"Son, W., Lee, J., Kim, M.S.: Generic Bell inequalities for multipartite arbitrary dimensional systems. Phys. Rev. Lett. 96, 060406 (2006)","DOI":"10.1103\/PhysRevLett.96.060406"},{"key":"3713_CR13","doi-asserted-by":"crossref","unstructured":"Collins, D., Gisin, N., Linden, N., Massar, S., Popescu, S.: Bell inequalities for arbitrarily high-dimensional systems. Phys. Rev. Lett. 88, 040404 (2002)","DOI":"10.1103\/PhysRevLett.88.040404"},{"key":"3713_CR14","doi-asserted-by":"crossref","unstructured":"Kwiat, P.G.: Hyper-entangled states. J. Mod. Opt. 44, 2173 (1997)","DOI":"10.1080\/09500349708231877"},{"key":"3713_CR15","doi-asserted-by":"crossref","unstructured":"Barreiro, J.T., Langford, N.K., Peters, N.A., Kwiat, P.G.: Generation of hyperentangled photon pairs. Phys. Rev. Lett. 95, 260501 (2005)","DOI":"10.1103\/PhysRevLett.95.260501"},{"key":"3713_CR16","doi-asserted-by":"crossref","unstructured":"Chen, K., Li, C.-M., Zhang, Q., Chen, Y.-A., Goebel, A., Chen, S., Mair, A., Pan, J.-W.: Experimental realization of one-way quantum computing with two-photon four-qubit cluster states. Phys. Rev. Lett. 99, 120503 (2007)","DOI":"10.1103\/PhysRevLett.99.120503"},{"key":"3713_CR17","doi-asserted-by":"crossref","unstructured":"Vaziri, A., Weihs, G., Zeilinger, A.: Experimental two-photon, three-dimensional entanglement for quantum communication. Phys. Rev. Lett. 89, 240401 (2002)","DOI":"10.1103\/PhysRevLett.89.240401"},{"key":"3713_CR18","doi-asserted-by":"crossref","unstructured":"Thew, R.T., Ac\u00edn, A., Zbinden, H., Gisin, N.: Bell-type test of energy-time entangled qutrits. Phys. Rev. Lett. 93, 010503 (2004)","DOI":"10.1103\/PhysRevLett.93.010503"},{"key":"3713_CR19","doi-asserted-by":"crossref","unstructured":"V\u00e9rtesi, T., Pironio, S., Brunner, N.: Closing the detection loophole in Bell experiments using qudits. Phys. Rev. Lett. 104, 060401 (2010)","DOI":"10.1103\/PhysRevLett.104.060401"},{"key":"3713_CR20","doi-asserted-by":"crossref","unstructured":"Ecker, S., Bouchard, F., Bulla, L., Brandt, F., Kohout, O., Steinlechner, F., Fickler, R., Malik, M., Guryanova, Y., Ursin, R., Huber, M.: Overcoming noise in entanglement distribution. Phys. Rev. X 9, 041042 (2019)","DOI":"10.1103\/PhysRevX.9.041042"},{"key":"3713_CR21","doi-asserted-by":"crossref","unstructured":"Zhu, F., Tyler, M., Valencia, N.H., Malik, M., Leach, J.: Is high-dimensional photonic entanglement robust to noise? AVS Quantum Sci. 3, 011401 (2021)","DOI":"10.1116\/5.0033889"},{"key":"3713_CR22","doi-asserted-by":"crossref","unstructured":"Dada, A.C., Leach, J., Buller, G.S., Padgett, M.J., Andersson, E.: Experimental high-dimensional two-photon entanglement and violations of generalized Bell inequalities. Nat. Phys. 7, 677 (2011)","DOI":"10.1038\/nphys1996"},{"key":"3713_CR23","doi-asserted-by":"crossref","unstructured":"Malik, M., Erhard, M., Huber, M., Krenn, M., Fickler, R., Zeilinger, A.: Multi-photon entanglement in high dimensions. Nat. Photonics 10, 248 (2016)","DOI":"10.1038\/nphoton.2016.12"},{"key":"3713_CR24","doi-asserted-by":"crossref","unstructured":"Kues, M., Reimer, C., Roztocki, P., Cortes, L.R., Sciara, S., Wetzel, B., Zhang, Y., Cino, A., Chu, S.T., Little, B.E., Moss, D.J., Caspani, L., Azana, J., Morandotti, R.: On-chip generation of high-dimensional entangled quantum states and their coherent control. Nature 546, 622 (2017)","DOI":"10.1038\/nature22986"},{"key":"3713_CR25","doi-asserted-by":"crossref","unstructured":"Wang, J., Paesani, S., Ding, Y., Santagati, R., Skrzypczyk, P., Salavrakos, A., Tura, J., Augusiak, R., Man\u010dinska, L., Bacco, D., Bonneau, D., Silverstone, J.W., Gong, Q., Ac\u00edn, A., Rottwitt, K., Oxenl\u00f8we, L.K., O\u2019Brien, J.L., Laing, A., Thompson, M.G.: Multidimensional quantum entanglement with large-scale integrated optics. Science 360, 285 (2018)","DOI":"10.1126\/science.aar7053"},{"key":"3713_CR26","doi-asserted-by":"crossref","unstructured":"Valencia, N.H., Goel, S., McCutcheon, W., Defienne, H., Malik, M.: Unscrambling entanglement through a complex medium. Nat. Phys. 16, 1112 (2020)","DOI":"10.1038\/s41567-020-0970-1"},{"key":"3713_CR27","doi-asserted-by":"crossref","unstructured":"Bourennane, M., Eibl, M., Kurtsiefer, C., Gaertner, S., Weinfurter, H., G\u00fchne, O., Hyllus, P., Bru\u00df, D., Lewenstein, M., Sanpera, A.: Experimental detection of multipartite entanglement using witness operators. Phys. Rev. Lett. 92, 087902 (2004)","DOI":"10.1103\/PhysRevLett.92.087902"},{"key":"3713_CR28","doi-asserted-by":"crossref","unstructured":"T\u00f3th, G., G\u00fchne, O.: Detecting genuine multipartite entanglement with two local measurements. Phys. Rev. Lett. 94, 060501 (2005)","DOI":"10.1103\/PhysRevLett.94.060501"},{"key":"3713_CR29","doi-asserted-by":"crossref","unstructured":"Vallone, G., Ceccarelli, R., Martini, F.D., Mataloni, P.: Hyperentanglement witness. Phys. Rev. A 78, 062305 (2008)","DOI":"10.1103\/PhysRevA.78.062305"},{"key":"3713_CR30","doi-asserted-by":"crossref","unstructured":"Huber, M., Mintert, F., Gabriel, A., Hiesmayr, B.C.: Detection of high-dimensional genuine multipartite entanglement of mixed states. Phys. Rev. Lett. 104, 210501 (2010)","DOI":"10.1103\/PhysRevLett.104.210501"},{"key":"3713_CR31","doi-asserted-by":"crossref","unstructured":"Kraft, T., Ritz, C., Brunner, N., Huber, M., G\u00fchne, O.: Characterizing genuine multilevel entanglement. Phys. Rev. Lett. 120, 060502 (2018)","DOI":"10.1103\/PhysRevLett.120.060502"},{"key":"3713_CR32","doi-asserted-by":"crossref","unstructured":"Walborn, S.P., Souto Ribeiro, P.H., Davidovich, L., Mintert, F., Buchleitner, A.: Experimental determination of entanglement with a single measurement. Nature 440, 1022 (2006)","DOI":"10.1038\/nature04627"},{"key":"3713_CR33","doi-asserted-by":"crossref","unstructured":"Guo, Y., Hu, X.-M., Liu, B.-H., Huang, Y.-F., Li, C.-F., Guo, G.-C.: Experimental witness of genuine high-dimensional entanglement. Phys. Rev. A 97, 062309 (2018)","DOI":"10.1103\/PhysRevA.97.062309"},{"key":"3713_CR34","doi-asserted-by":"crossref","unstructured":"Martin, A., Guerreiro, T., Tiranov, A., Designolle, S., Fr\u00ebwis, F., Brunner, N., Huber, M., Gisin, N.: Quantifying photonic high-dimensional entanglement. Phys. Rev. Lett. 118, 110501 (2017)","DOI":"10.1103\/PhysRevLett.118.110501"},{"key":"3713_CR35","doi-asserted-by":"crossref","unstructured":"Tiranov, A., Designolle, S., Cruzeiro, E.Z., Lavoie, J., Brunner, N., Afzelius, M., Huber, M., Gisin, N.: Quantification of multidimensional entanglement stored in a crystal. Phys. Rev. A 96, 040303 (2017)","DOI":"10.1103\/PhysRevA.96.040303"},{"key":"3713_CR36","doi-asserted-by":"crossref","unstructured":"Bavaresco, J., Valencia, N.H., Kl\u00f6ckl, C., Pivoluska, M., Erker, P., Friis, N., Malik, M., Huber, M.: Measurements in two bases are sufficient for certifying high-dimensional entanglement. Nat. Phys. 14, 1032 (2018)","DOI":"10.1038\/s41567-018-0203-z"},{"key":"3713_CR37","doi-asserted-by":"crossref","unstructured":"M. Da\u0327browski, M. Mazelanik, M. Parniak, A. Leszczy\u0144ski, M. Lipka, and W. Wasilewski,: Certification of high-dimensional entanglement and Einstein\u2013Podolsky\u2013Rosen steering with cold atomic quantum memory. Phys. Rev. A 98, 042126 (2018)","DOI":"10.1103\/PhysRevA.98.042126"},{"key":"3713_CR38","doi-asserted-by":"crossref","unstructured":"Schneeloch, J., Tison, C.C., Fanto, M.L., Alsing, P.M., Howland, G.A.: Quantifying entanglement in a 8-billion-dimensional quantum state space. Nat. Commun. 10, 248 (2019)","DOI":"10.1038\/s41467-019-10810-z"},{"key":"3713_CR39","doi-asserted-by":"crossref","unstructured":"Valencia, N.H., Srivastav, V., Pivoluska, M., Huber, M., Friis, N., McCutcheon, W., Malik, M.: High-dimensional pixel entanglement: efficient generation and certification. Quantum 4, 376 (2020)","DOI":"10.22331\/q-2020-12-24-376"},{"key":"3713_CR40","doi-asserted-by":"crossref","unstructured":"Altepeter, J.B., Jeffrey, E.R., Kwiat, P.G.: Photonic state tomography. Adv. At. Mol. Opt. Phys. 52, 105\u2013159 (2005)","DOI":"10.1016\/S1049-250X(05)52003-2"},{"key":"3713_CR41","doi-asserted-by":"crossref","unstructured":"Ahrens, J., Badzia, P., Cabello, A., Bourennane, M.: Experimental device-independent tests of classical and quantum dimensions. Nat. Phys. 8, 592 (2012)","DOI":"10.1038\/nphys2333"},{"key":"3713_CR42","doi-asserted-by":"crossref","unstructured":"Terhal, B.M.: Bell inequalities and the separability criterion. Phys. Lett. A 271, 319 (2000)","DOI":"10.1016\/S0375-9601(00)00401-1"},{"key":"3713_CR43","doi-asserted-by":"crossref","unstructured":"G\u00fchne, O., T\u00f3th, G.: Entanglement detection. Phys. Rep. 474, 1 (2009)","DOI":"10.1016\/j.physrep.2009.02.004"},{"key":"3713_CR44","doi-asserted-by":"crossref","unstructured":"Peres, A.: Higher order Schmidt decompositions. Phys. Lett. A 202, 16 (1995)","DOI":"10.1016\/0375-9601(95)00315-T"},{"key":"3713_CR45","doi-asserted-by":"crossref","unstructured":"Hu, X.-M., Huang, C.-X., Sheng, Y.-B., Zhou, L., Liu, B.-H., Guo, Y., Zhang, C., Xing, W.-B., Huang, Y.-F., Li, C.-F., Guo, G.-C.: Long-distance entanglement purification for quantum communication. Phys. Rev. Lett. 126, 010503 (2021)","DOI":"10.1103\/PhysRevLett.126.010503"},{"key":"3713_CR46","doi-asserted-by":"crossref","unstructured":"Huang, C.-X., Hu, X.-M., Liu, B.-H., Zhou, L., Sheng, Y.-B., Li, C.-F., Guo, G.-C.: Experimental one-step deterministic polarization entanglement purification. Sci. Bull. 67, 593 (2022)","DOI":"10.1016\/j.scib.2021.12.018"},{"key":"3713_CR47","doi-asserted-by":"crossref","unstructured":"Yan, P.-S., Zhou, L., Zhong, W., Sheng, Y.-B.: Measurement-based logical qubit entanglement purification. Phys. Rev. A 105, 062418 (2022)","DOI":"10.1103\/PhysRevA.105.062418"},{"key":"3713_CR48","unstructured":"Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)"},{"key":"3713_CR49","doi-asserted-by":"crossref","unstructured":"D\u00fcr, W., Cirac, J.I.: Classification of multiqubit mixed states: separability and distillability properties. Phys. Rev. A 61, 042314 (2000)","DOI":"10.1103\/PhysRevA.61.042314"},{"key":"3713_CR50","doi-asserted-by":"crossref","unstructured":"Nielsen, M.A., Kempe, J.: Separable states are more disordered globally than locally. Phys. Rev. Lett. 86, 5184 (2001)","DOI":"10.1103\/PhysRevLett.86.5184"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03713-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03713-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03713-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,19]],"date-time":"2022-11-19T17:13:33Z","timestamp":1668878013000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03713-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,1]]},"references-count":50,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["3713"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03713-4","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2022,11,1]]},"assertion":[{"value":"25 August 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 October 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 November 2022","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 have no relevant financial or non-financial interests to disclose, and this manuscript has no associated data.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"364"}}