{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,24]],"date-time":"2026-02-24T15:55:24Z","timestamp":1771948524069,"version":"3.50.1"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T00:00:00Z","timestamp":1739836800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T00:00:00Z","timestamp":1739836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62272056, 62372048, 62371069"],"award-info":[{"award-number":["62272056, 62372048, 62371069"]}],"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":["62272056, 62372048, 62371069"],"award-info":[{"award-number":["62272056, 62372048, 62371069"]}],"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":["62272056, 62372048, 62371069"],"award-info":[{"award-number":["62272056, 62372048, 62371069"]}],"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":["62272056, 62372048, 62371069"],"award-info":[{"award-number":["62272056, 62372048, 62371069"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04672-2","type":"journal-article","created":{"date-parts":[[2025,2,18]],"date-time":"2025-02-18T08:44:08Z","timestamp":1739868248000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["A (t,\u00a0n) threshold quantum secret sharing with authentication based on single photons"],"prefix":"10.1007","volume":"24","author":[{"given":"Jie","family":"Zhang","sequence":"first","affiliation":[]},{"given":"Jie","family":"Zhang","sequence":"additional","affiliation":[]},{"given":"Sujuan","family":"Qin","sequence":"additional","affiliation":[]},{"given":"Zhengping","family":"Jin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,2,18]]},"reference":[{"issue":"11","key":"4672_CR1","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1145\/359168.359176","volume":"22","author":"A Shamir","year":"1979","unstructured":"Shamir, A.: How to share a secret. Commun. ACM 22(11), 612\u2013613 (1979)","journal-title":"Commun. ACM"},{"key":"4672_CR2","doi-asserted-by":"crossref","unstructured":"Blakley, G.R.: Safeguarding cryptographic keys. In: managing requirements knowledge, international workshop on, pp. 313\u2013313 (1979)","DOI":"10.1109\/MARK.1979.8817296"},{"issue":"9","key":"4672_CR3","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1038\/nphys3029","volume":"10","author":"S Lloyd","year":"2014","unstructured":"Lloyd, S., Mohseni, M., Rebentrost, P.: Quantum principal component analysis. Nat. Phys. 10(9), 631\u2013633 (2014)","journal-title":"Nat. Phys."},{"key":"4672_CR4","unstructured":"Otterbach, J.S., Manenti, R., Alidoust, N., Bestwick, A., Block, M., Bloom, B., Caldwell, S., Didier, N., Fried, E.S., Hong, S., et al.: Unsupervised machine learning on a hybrid quantum computer. Preprint at arxiv:1712.05771 (2017)"},{"issue":"4","key":"4672_CR5","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.103.042415","volume":"103","author":"I Kerenidis","year":"2021","unstructured":"Kerenidis, I., Landman, J.: Quantum spectral clustering. Phys. Rev. A 103(4), 042415 (2021)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"4672_CR6","volume":"102","author":"S-J Pan","year":"2020","unstructured":"Pan, S.-J., Wan, L.-C., Liu, H.-L., Wang, Q.-L., Qin, S.-J., Wen, Q.-Y., Gao, F.: Improved quantum algorithm for a-optimal projection. Phys. Rev. A 102(5), 052402 (2020)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"4672_CR7","volume":"31","author":"S-J Pan","year":"2022","unstructured":"Pan, S.-J., Wan, L.-C., Liu, H.-L., Wu, Y.-S., Qin, S.-J., Wen, Q.-Y., Gao, F.: Quantum algorithm for neighborhood preserving embedding. Chin. Phys. B 31(6), 060304 (2022)","journal-title":"Chin. Phys. B"},{"issue":"6","key":"4672_CR8","volume":"97","author":"L-C Wan","year":"2018","unstructured":"Wan, L.-C., Yu, C.-H., Pan, S.-J., Gao, F., Wen, Q.-Y., Qin, S.-J.: Asymptotic quantum algorithm for the Toeplitz systems. Phys. Rev. A 97(6), 062322 (2018)","journal-title":"Phys. Rev. A"},{"issue":"7","key":"4672_CR9","doi-asserted-by":"crossref","first-page":"2300031","DOI":"10.1002\/qute.202300031","volume":"6","author":"H-L Liu","year":"2023","unstructured":"Liu, H.-L., Wan, L.-C., Yu, C.-H., Pan, S.-J., Qin, S.-J., Gao, F., Wen, Q.-Y.: A quantum algorithm for solving eigenproblem of the Laplacian matrix of a fully connected weighted graph. Adv. Quantum. Technol. 6(7), 2300031 (2023)","journal-title":"Adv. Quantum. Technol."},{"issue":"5","key":"4672_CR10","volume":"67","author":"Y-Q Song","year":"2024","unstructured":"Song, Y.-Q., Wu, Y.-S., Wu, S.-Y., Li, D.-D., Wen, Q.-Y., Qin, S.-J., Gao, F.: A quantum federated learning framework for classical clients. Sci. China Phys., Mech. Astron. 67(5), 250311 (2024)","journal-title":"Sci. China Phys., Mech. Astron."},{"key":"4672_CR11","doi-asserted-by":"crossref","first-page":"1362690","DOI":"10.3389\/fphy.2024.1362690","volume":"12","author":"Y-Q Song","year":"2024","unstructured":"Song, Y.-Q., Li, J., Wu, Y.-S., Qin, S.-J., Wen, Q.-Y., Gao, F.: A resource-efficient quantum convolutional neural network. Front. Phys. 12, 1362690 (2024)","journal-title":"Front. Phys."},{"key":"4672_CR12","volume":"633","author":"L-Z Qin","year":"2024","unstructured":"Qin, L.-Z., Liu, B., Gao, F., Huang, W., Xu, B.-J., Li, Y.: Decoy-state quantum private query protocol with two-way communication. Phys. A 633, 129427 (2024)","journal-title":"Phys. A"},{"issue":"6","key":"4672_CR13","doi-asserted-by":"crossref","first-page":"2400078","DOI":"10.1002\/qute.202400078","volume":"7","author":"Y Zhang","year":"2024","unstructured":"Zhang, Y., Yao, Y., Sun, H.-X., Zhang, K.-J., Song, T.-T.: A new hybrid protocol that simultaneously achieves quantum multiparty summation and ranking. Adv. Quantum. Technol. 7(6), 2400078 (2024)","journal-title":"Adv. Quantum. Technol."},{"key":"4672_CR14","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.tcs.2014.05.025","volume":"560","author":"CH Bennett","year":"2014","unstructured":"Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. Theoret. Comput. Sci. 560, 7\u201311 (2014)","journal-title":"Theoret. Comput. Sci."},{"issue":"8","key":"4672_CR15","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1038\/s41566-021-00828-5","volume":"15","author":"J-P Chen","year":"2021","unstructured":"Chen, J.-P., Zhang, C., Liu, Y., Jiang, C., Zhang, W.-J., Han, Z.-Y., Ma, S.-Z., Hu, X.-L., Li, Y.-H., Liu, H., et al.: Twin-field quantum key distribution over a 511 km optical fibre linking two distant metropolitan areas. Nat. Photonics 15(8), 570\u2013575 (2021)","journal-title":"Nat. Photonics"},{"issue":"3","key":"4672_CR16","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1109\/JSTQE.2014.2358192","volume":"21","author":"F Gao","year":"2014","unstructured":"Gao, F., Liu, B., Huang, W., Wen, Q.-Y.: Postprocessing of the oblivious key in quantum private query. IEEE J. Sel. Top. Quantum Electron. 21(3), 98\u2013108 (2014)","journal-title":"IEEE J. Sel. Top. Quantum Electron."},{"issue":"23","key":"4672_CR17","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.100.230502","volume":"100","author":"V Giovannetti","year":"2008","unstructured":"Giovannetti, V., Lloyd, S., Maccone, L.: Quantum private queries. Phys. Rev. Lett. 100(23), 230502 (2008)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"4672_CR18","volume":"78","author":"S Lin","year":"2008","unstructured":"Lin, S., Wen, Q.-Y., Gao, F., Zhu, F.-C.: Quantum secure direct communication with $$\\chi $$-type entangled states. Phys. Rev. A 78(6), 064304 (2008)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"4672_CR19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1038\/s41377-021-00634-2","volume":"10","author":"Z-T Qi","year":"2021","unstructured":"Qi, Z.-T., Li, Y.-H., Huang, Y.-W., Feng, J., Zheng, Y.-L., Chen, X.-F.: A 15-user quantum secure direct communication network. Light: Sci. Appl. 10(1), 183 (2021)","journal-title":"Light: Sci. Appl."},{"issue":"2","key":"4672_CR20","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11128-022-03817-x","volume":"22","author":"X Zhang","year":"2023","unstructured":"Zhang, X., Wei, C.-Y., Qin, S.-J., Gao, F., Wen, Q.-Y.: Practical efficient 1-out-of-n quantum oblivious transfer protocol. Quantum Inf. Process. 22(2), 99 (2023)","journal-title":"Quantum Inf. Process."},{"key":"4672_CR21","doi-asserted-by":"crossref","unstructured":"Cr\u00e9peau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing, pp. 643\u2013652 (2002)","DOI":"10.1145\/509907.510000"},{"issue":"4","key":"4672_CR22","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/s11128-019-2233-6","volume":"18","author":"S Mashhadi","year":"2019","unstructured":"Mashhadi, S.: General secret sharing based on quantum Fourier transform. Quantum Inf. Process. 18(4), 114 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"4672_CR23","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0375-9601(03)00074-4","volume":"310","author":"G-P Guo","year":"2003","unstructured":"Guo, G.-P., Guo, G.-C.: Quantum secret sharing without entanglement. Phys. Lett. A 310(4), 247\u2013251 (2003)","journal-title":"Phys. Lett. A"},{"issue":"3","key":"4672_CR24","doi-asserted-by":"crossref","first-page":"1829","DOI":"10.1103\/PhysRevA.59.1829","volume":"59","author":"M Hillery","year":"1999","unstructured":"Hillery, M., Bu\u017eek, V., Berthiaume, A.: Quantum secret sharing. Phys. Revi. A 59(3), 1829 (1999)","journal-title":"Phys. Revi. A"},{"issue":"1","key":"4672_CR25","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1103\/PhysRevA.59.162","volume":"59","author":"A Karlsson","year":"1999","unstructured":"Karlsson, A., Koashi, M., Imoto, N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59(1), 162 (1999)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"4672_CR26","doi-asserted-by":"crossref","first-page":"648","DOI":"10.1103\/PhysRevLett.83.648","volume":"83","author":"R Cleve","year":"1999","unstructured":"Cleve, R., Gottesman, D., Lo, H.-K.: How to share a quantum secret. Phys. Rev. Lett. 83(3), 648 (1999)","journal-title":"Phys. Rev. Lett."},{"issue":"7","key":"4672_CR27","volume":"33","author":"C-M Bai","year":"2024","unstructured":"Bai, C.-M., Liu, L., Zhang, S.-J.: Verifiable quantum secret sharing scheme based on orthogonal product states. Chin. Phys. B 33(7), 070302 (2024)","journal-title":"Chin. Phys. B"},{"key":"4672_CR28","doi-asserted-by":"publisher","DOI":"10.1142\/S021974992450045X","author":"C-M Bai","year":"2024","unstructured":"Bai, C.-M., Zhang, S.-J., Liu, L.: Verifiable quantum secret sharing scheme using bell states for a class of special access structures. Int. J. Quantum Inf. (2024). https:\/\/doi.org\/10.1142\/S021974992450045X","journal-title":"Int. J. Quantum Inf."},{"key":"4672_CR29","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1007\/s11128-011-0323-1","volume":"11","author":"Y-G Yang","year":"2012","unstructured":"Yang, Y.-G., Jia, X., Wang, H.-Y., Zhang, H.: Verifiable quantum (k, n)-threshold secret sharing. Quantum Inf. Process. 11, 1619\u20131625 (2012)","journal-title":"Quantum Inf. Process."},{"key":"4672_CR30","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-017-1770-0","volume":"17","author":"C Lu","year":"2018","unstructured":"Lu, C., Miao, F., Hou, J., Meng, K.: Verifiable threshold quantum secret sharing with sequential communication. Quantum Inf. Process. 17, 1\u201313 (2018)","journal-title":"Quantum Inf. Process."},{"key":"4672_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-019-2494-0","volume":"19","author":"C-W Yang","year":"2020","unstructured":"Yang, C.-W., Tsai, C.-W.: Efficient and secure dynamic quantum secret sharing protocol based on bell states. Quantum Inf. Process. 19, 1\u201314 (2020)","journal-title":"Quantum Inf. Process."},{"key":"4672_CR32","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1007\/s11128-014-0779-x","volume":"13","author":"C-H Liao","year":"2014","unstructured":"Liao, C.-H., Yang, C.-W., Hwang, T.: Dynamic quantum secret sharing protocol based on Ghz state. Quantum Inf. Process. 13, 1907\u20131916 (2014)","journal-title":"Quantum Inf. Process."},{"key":"4672_CR33","volume":"624","author":"Z You","year":"2023","unstructured":"You, Z., Wang, Y., Dou, Z., Li, J., Chen, X., Li, L.: Dynamic quantum secret sharing between multiparty and multiparty based on single photons. Phys. A 624, 128893 (2023)","journal-title":"Phys. A"},{"key":"4672_CR34","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11128-013-0716-4","volume":"13","author":"R-K Chen","year":"2014","unstructured":"Chen, R.-K., Zhang, Y.-Y., Shi, J.-H., Li, F.-G.: A multiparty error-correcting method for quantum secret sharing. Quantum Inf. Process. 13, 21\u201331 (2014)","journal-title":"Quantum Inf. Process."},{"issue":"2","key":"4672_CR35","doi-asserted-by":"crossref","first-page":"58","DOI":"10.1007\/s11128-024-04265-5","volume":"23","author":"S Gupta","year":"2024","unstructured":"Gupta, S., Sinha, A., Pandey, S.K.: A resilient m-qubit quantum secret sharing scheme using quantum error correction code. Quantum Inf. Process. 23(2), 58 (2024)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"4672_CR36","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1007\/s10773-023-05533-3","volume":"63","author":"C-M Bai","year":"2024","unstructured":"Bai, C.-M., Feng, Y., Zhang, S., Liu, L.: Verifiable quantum secret sharing scheme based on LDPC codes. Int. J. Theor. Phys. 63(1), 6 (2024)","journal-title":"Int. J. Theor. Phys."},{"issue":"10","key":"4672_CR37","volume":"31","author":"X-X Ju","year":"2022","unstructured":"Ju, X.-X., Zhong, W., Sheng, Y.-B., Zhou, L.: Measurement-device-independent quantum secret sharing with hyper-encoding. Chin. Phys. B 31(10), 100302 (2022)","journal-title":"Chin. Phys. B"},{"issue":"1","key":"4672_CR38","volume":"100","author":"S Roy","year":"2019","unstructured":"Roy, S., Mukhopadhyay, S.: Device-independent quantum secret sharing in arbitrary even dimensions. Phys. Rev. A 100(1), 012319 (2019)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"4672_CR39","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.101.052339","volume":"101","author":"M Moreno","year":"2020","unstructured":"Moreno, M., Brito, S., Nery, R.V., Chaves, R.: Device-independent secret sharing and a stronger form of bell nonlocality. Phys. Rev. A 101(5), 052339 (2020)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4672_CR40","doi-asserted-by":"crossref","DOI":"10.2991\/978-94-6463-463-1","volume":"110","author":"Q Zhang","year":"2024","unstructured":"Zhang, Q., Zhong, W., Du, M.-M., Shen, S.-T., Li, X.-Y., Zhang, A.-L., Zhou, L., Sheng, Y.-B.: Device-independent quantum secret sharing with noise preprocessing and postselection. Phys. Rev. A 110(4), 042403 (2024)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"4672_CR41","first-page":"1","volume":"5","author":"B Bell","year":"2014","unstructured":"Bell, B., Markham, D., Herrera-Mart\u00ed, D., Marin, A., Wadsworth, W., Rarity, J., Tame, M.: Experimental demonstration of graph-state quantum secret sharing. Nat. Commun. 5(1), 1\u201312 (2014)","journal-title":"Nat. Commun."},{"issue":"1","key":"4672_CR42","doi-asserted-by":"crossref","first-page":"15645","DOI":"10.1038\/ncomms15645","volume":"8","author":"Y Cai","year":"2017","unstructured":"Cai, Y., Roslund, J., Ferrini, G., Arzani, F., Xu, X., Fabre, C., Treps, N.: Multimode entanglement in reconfigurable graph states using optical frequency combs. Nat. Commun. 8(1), 15645 (2017)","journal-title":"Nat. Commun."},{"issue":"15","key":"4672_CR43","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.121.150502","volume":"121","author":"Y Zhou","year":"2018","unstructured":"Zhou, Y., Yu, J., Yan, Z., Jia, X., Zhang, J., Xie, C., Peng, K.: Quantum secret sharing among four players using multipartite bound entanglement of an optical field. Phys. Rev. Lett. 121(15), 150502 (2018)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"4672_CR44","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.67.044302","volume":"67","author":"S Bagherinezhad","year":"2003","unstructured":"Bagherinezhad, S., Karimipour, V.: Quantum secret sharing based on reusable greenberger-horne-zeilinger states as secure carriers. Phys. Rev. A 67(4), 044302 (2003)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"4672_CR45","volume":"72","author":"F Gao","year":"2005","unstructured":"Gao, F., Guo, F.-Z., Wen, Q.-Y., Zhu, F.-C.: Comment on \u201cquantum secret sharing based on reusable greenberger-horne-zeilinger states as secure carriers\u2019\u2019. Phys. Rev. A 72(3), 036302 (2005)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"4672_CR46","volume":"74","author":"J-Z Du","year":"2006","unstructured":"Du, J.-Z., Qin, S.-J., Wen, Q.-Y., Zhu, F.-C.: Comment ii on \u201cquantum secret sharing based on reusable greenberger-horne-zeilinger states as secure carriers\u2019\u2019. Phys. Rev. A 74(1), 016301 (2006)","journal-title":"Phys. Rev. A"},{"issue":"8","key":"4672_CR47","doi-asserted-by":"crossref","first-page":"4689","DOI":"10.7498\/aps.57.4689","volume":"57","author":"Y Sun","year":"2008","unstructured":"Sun, Y., Du, J.-Z., Qin, S.-J., Wen, Q.-Y., Zhu, F.-C., et al.: Quantum secret sharing with bidirectional authentication. Acta Phys. Sin. 57(8), 4689\u20134694 (2008)","journal-title":"Acta Phys. Sin."},{"issue":"4","key":"4672_CR48","doi-asserted-by":"crossref","first-page":"1750023","DOI":"10.1142\/S021974991750023X","volume":"15","author":"H Abulkasim","year":"2017","unstructured":"Abulkasim, H., Hamad, S., Khalifa, A., El Bahnasy, K.: Quantum secret sharing with identity authentication based on bell states. Int. J. Quantum Inf. 15(4), 1750023 (2017)","journal-title":"Int. J. Quantum Inf."},{"issue":"7","key":"4672_CR49","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/s11128-022-03617-3","volume":"21","author":"F-L Li","year":"2022","unstructured":"Li, F.-L., Hu, H., Zhu, S.-X., Yan, J.-Y., Ding, J.: A verifiable (k, n)-threshold dynamic quantum secret sharing scheme. Quantum Inf. Process. 21(7), 259 (2022)","journal-title":"Quantum Inf. Process."},{"issue":"2","key":"4672_CR50","volume":"71","author":"L-Y Hsu","year":"2005","unstructured":"Hsu, L.-Y., Li, C.-M.: Quantum secret sharing using product states. Phys. Rev. A 71(2), 022321 (2005)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4672_CR51","volume":"71","author":"Z-J Zhang","year":"2005","unstructured":"Zhang, Z.-J., Li, Y., Man, Z.-X.: Multiparty quantum secret sharing. Phys. Rev. A 71(4), 044301 (2005)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"4672_CR52","volume":"72","author":"F-G Deng","year":"2005","unstructured":"Deng, F.-G., Li, X.-H., Zhou, H.-Y., Zhang, Z.-J.: Improving the security of multiparty quantum secret sharing against trojan horse attack. Phys. Rev. A 72(4), 044302 (2005)","journal-title":"Phys. Rev. A"},{"issue":"2","key":"4672_CR53","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1016\/j.physleta.2006.04.030","volume":"357","author":"S-J Qin","year":"2006","unstructured":"Qin, S.-J., Gao, F., Wen, Q.-Y., Zhu, F.-C.: Improving the security of multiparty quantum secret sharing against an attack with a fake signal. Phys. Lett. A 357(2), 101\u2013103 (2006)","journal-title":"Phys. Lett. A"},{"issue":"9","key":"4672_CR54","doi-asserted-by":"crossref","first-page":"2690","DOI":"10.1016\/j.optcom.2007.12.045","volume":"281","author":"L-F Han","year":"2008","unstructured":"Han, L.-F., Liu, Y.-M., Liu, J., Zhang, Z.-J.: Multiparty quantum secret sharing of secure direct communication using single photons. Opt. Commun. 281(9), 2690\u20132694 (2008)","journal-title":"Opt. Commun."},{"issue":"23","key":"4672_CR55","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.95.230505","volume":"95","author":"C Schmid","year":"2005","unstructured":"Schmid, C., Trojek, P., Bourennane, M., Kurtsiefer, C., \u017bukowski, M., Weinfurter, H.: Experimental single qubit quantum secret sharing. Phys. Rev. Lett. 95(23), 230505 (2005)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"4672_CR56","volume":"98","author":"GP He","year":"2007","unstructured":"He, G.P.: Comment on \u201cexperimental single qubit quantum secret sharing\u2019\u2019. Phys. Rev. Lett. 98(2), 028901 (2007)","journal-title":"Phys. Rev. Lett."},{"issue":"3","key":"4672_CR57","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevA.92.030302","volume":"92","author":"A Tavakoli","year":"2015","unstructured":"Tavakoli, A., Herbauts, I., \u017bukowski, M., Bourennane, M.: Secret sharing with a single d-level quantum system. Phys. Rev. A 92(3), 030302 (2015)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"4672_CR58","volume":"92","author":"V Karimipour","year":"2015","unstructured":"Karimipour, V., Asoudeh, M.: Quantum secret sharing and random hopping: using single states instead of entanglement. Phys. Rev. A 92(3), 030301 (2015)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"4672_CR59","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1140\/epjqt\/s40507-023-00186-x","volume":"10","author":"S-Y Kuo","year":"2023","unstructured":"Kuo, S.-Y., Tseng, K.-C., Yang, C.-C., Chou, Y.-H.: Efficient multiparty quantum secret sharing based on a novel structure and single qubits. EPJ Quantum Technol. 10(1), 29 (2023)","journal-title":"EPJ Quantum Technol."},{"key":"4672_CR60","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1007\/s11467-007-0050-3","volume":"2","author":"G-L Long","year":"2007","unstructured":"Long, G.-L., Deng, F.-G., Wang, C., Li, X.-H., Wen, K., Wang, W.-Y.: Quantum secure direct communication and deterministic secure quantum communication. Front. Phys China 2, 251\u2013272 (2007)","journal-title":"Front. Phys China"},{"issue":"22","key":"4672_CR61","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.118.220501","volume":"118","author":"W Zhang","year":"2017","unstructured":"Zhang, W., Ding, D.-S., Sheng, Y.-B., Zhou, L., Shi, B.-S., Guo, G.-C.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118(22), 220501 (2017)","journal-title":"Phys. Rev. Lett."},{"issue":"2","key":"4672_CR62","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1007\/s11128-023-03853-1","volume":"22","author":"Y-P Hong","year":"2023","unstructured":"Hong, Y.-P., Zhou, L., Zhong, W., Sheng, Y.-B.: Measurement-device-independent three-party quantum secure direct communication. Quantum Inf. Process. 22(2), 111 (2023)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"4672_CR63","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1007\/s11128-024-04397-8","volume":"23","author":"P Roy","year":"2024","unstructured":"Roy, P., Bera, S., Gupta, S., Majumdar, A.S.: Device-independent quantum secure direct communication under non-markovian quantum channels. Quantum Inf. Process. 23(5), 170 (2024)","journal-title":"Quantum Inf. Process."},{"issue":"1","key":"4672_CR64","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjqt\/s40507-023-00211-z","volume":"11","author":"G Gao","year":"2024","unstructured":"Gao, G.: Cryptanalysis and improvement of efficient multiparty quantum secret sharing based on a novel structure and single qubits. EPJ Quantum Technol. 11(1), 1\u20138 (2024)","journal-title":"EPJ Quantum Technol."},{"key":"4672_CR65","first-page":"183","volume-title":"\u0152uvres de Lagrange","author":"JL Lagrange","year":"1877","unstructured":"Lagrange, J.L.: Le\u00e7ons \u00e9l\u00e9mentaires sur les math\u00e9matiques donn\u00e9es \u00e0 l\u2019\u00e9cole normale. In: Serret, J.-A. (ed.) \u0152uvres de Lagrange, pp. 183\u2013287. Gauthier-Villars, Paris, France (1877)"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04672-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04672-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04672-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T04:01:39Z","timestamp":1742184099000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04672-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,18]]},"references-count":65,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["4672"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04672-2","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,18]]},"assertion":[{"value":"31 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 January 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 February 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":"61"}}