{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T11:08:42Z","timestamp":1784286522958,"version":"3.55.0"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:00:00Z","timestamp":1779062400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T00:00:00Z","timestamp":1779062400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-026-05183-4","type":"journal-article","created":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T04:41:58Z","timestamp":1779079318000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Verifiable dynamic multiparty quantum secret sharing protocol based on orthogonal product states"],"prefix":"10.1007","volume":"25","author":[{"given":"Hang","family":"Guo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shuai","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,5,18]]},"reference":[{"issue":"2","key":"5183_CR1","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303\u2013332 (1999)","journal-title":"SIAM Rev."},{"key":"5183_CR2","doi-asserted-by":"crossref","unstructured":"Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing, pp. 212\u2013219 (1996)","DOI":"10.1145\/237814.237866"},{"issue":"11","key":"5183_CR3","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1007\/s11128-025-04969-2","volume":"24","author":"X Li","year":"2025","unstructured":"Li, X., Li, S., Li, J., Miao, L.: An entanglement-free authenticated quantum key distribution protocol. Quantum Inf. Process. 24(11), 367 (2025)","journal-title":"Quantum Inf. Process."},{"issue":"6","key":"5183_CR4","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/s11128-025-04780-z","volume":"24","author":"Z-J Chen","year":"2025","unstructured":"Chen, Z.-J., Hao, C.-P., Gong, L., Guo, J.-S., Wang, Y., Zhang, C.-M., Li, H.-W.: Improving the performance of quantum key distribution with weak-randomness basis selection. Quantum Inf. Process. 24(6), 162 (2025)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"5183_CR5","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1007\/s11128-025-04706-9","volume":"24","author":"C Yang","year":"2025","unstructured":"Yang, C., Wang, L., Jiao, R.: The performance of satellite-based mode-pairing quantum key distribution. Quantum Inf. Process. 24(3), 86 (2025)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"5183_CR6","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.68.042317","volume":"68","author":"F-G Deng","year":"2003","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(4), 042317 (2003)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"5183_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.69.052319","volume":"69","author":"F-G Deng","year":"2004","unstructured":"Deng, F.-G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)","journal-title":"Phys. Rev. A"},{"key":"5183_CR8","doi-asserted-by":"publisher","first-page":"0193","DOI":"10.34133\/research.0193","volume":"6","author":"Z Cao","year":"2023","unstructured":"Cao, Z., Lu, Y., Chai, G., Yu, H., Liang, K., Wang, L.: Realization of quantum secure direct communication with continuous variable. Research 6, 0193 (2023)","journal-title":"Research"},{"issue":"2","key":"5183_CR9","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevApplied.16.024012","volume":"16","author":"Z Cao","year":"2021","unstructured":"Cao, Z., Wang, L., Liang, K., Chai, G., Peng, J.: Continuous-variable quantum secure direct communication based on gaussian mapping. Phys. Rev. Appl. 16(2), 024012 (2021)","journal-title":"Phys. Rev. Appl."},{"issue":"4","key":"5183_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/s11433-025-2871-y","volume":"69","author":"Z Zuo","year":"2026","unstructured":"Zuo, Z., Liang, Z., Mao, N., Wang, Y., Guo, Y.: Continuous-variable quantum secure direct communication against dual-sequence gaussian attacks with quantum memory. Sci. China Phys. Mech. Astron. 69(4), 240314 (2026)","journal-title":"Sci. China Phys. Mech. Astron."},{"issue":"9","key":"5183_CR11","doi-asserted-by":"publisher","first-page":"1445","DOI":"10.1016\/j.scib.2025.02.038","volume":"70","author":"Y Yang","year":"2025","unstructured":"Yang, Y., Li, Y., Li, H.S., Wu, C., Zheng, Y., Chen, X.: A 300-km fully-connected quantum secure direct communication network. Sci. Bull. 70(9), 1445\u20131451 (2025)","journal-title":"Sci. Bull."},{"key":"5183_CR12","doi-asserted-by":"publisher","DOI":"10.1016\/j.fmre.2025.12.008","author":"J-W Ying","year":"2025","unstructured":"Ying, J.-W., Wang, J.-Y., Xiao, Y.-X., Gu, S.-P., Wang, X.-F., Zhou, L., Sheng, Y.-B.: Passive decoy state quantum secure direct communication. Fund. Res. (2025). https:\/\/doi.org\/10.1016\/j.fmre.2025.12.008","journal-title":"Fund. Res."},{"key":"5183_CR13","doi-asserted-by":"crossref","unstructured":"Paparelle, I., Mousavi, F., Scazza, F., Bassi, A., Paris, M., Zavatta, A.: Practical quantum secure direct communication with squeezed states. arXiv preprint arXiv:2306.14322 (2023)","DOI":"10.1109\/CLEO\/Europe-EQEC57999.2023.10231767"},{"issue":"8","key":"5183_CR14","doi-asserted-by":"publisher","first-page":"4627","DOI":"10.1126\/sciadv.adt4627","volume":"11","author":"D Pan","year":"2025","unstructured":"Pan, D., Liu, Y.-C., Niu, P., Zhang, H., Zhang, F., Wang, M., Song, X.-T., Chen, X., Zheng, C., Long, G.-L.: Simultaneous transmission of information and key exchange using the same photonic quantum states. Sci. Adv. 11(8), 4627 (2025)","journal-title":"Sci. Adv."},{"issue":"7","key":"5183_CR15","doi-asserted-by":"publisher","first-page":"179403:1","DOI":"10.1007\/s11432-025-4608-6","volume":"69","author":"L Wang","year":"2026","unstructured":"Wang, L., Chai, G., Cao, Z., Chen, X.: Highly reliable quantum secure direct communication based on concatenated GKP-QLDPC codes. Sci. China Inf. Sci. 69(7), 179403:1-179403:2 (2026)","journal-title":"Sci. China Inf. Sci."},{"issue":"3","key":"5183_CR16","doi-asserted-by":"publisher","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. Rev. A 59(3), 1829 (1999)","journal-title":"Phys. Rev. A"},{"issue":"15","key":"5183_CR17","doi-asserted-by":"publisher","DOI":"10.1103\/7wrk-p6gl","volume":"135","author":"Y-R Xiao","year":"2025","unstructured":"Xiao, Y.-R., Yin, H.-L., Hua, W.-J., Cao, X.-Y., Chen, Z.-B.: Experimental efficient source-independent quantum secret sharing against coherent attacks. Phys. Rev. Lett. 135(15), 150801 (2025)","journal-title":"Phys. Rev. Lett."},{"issue":"9","key":"5183_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.114.090501","volume":"114","author":"Y Fu","year":"2015","unstructured":"Fu, Y., Yin, H.-L., Chen, T.-Y., Chen, Z.-B.: Long-distance measurement-device-independent multiparty quantum communication. Phys. Rev. Lett. 114(9), 090501 (2015)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"5183_CR19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.111.012602","volume":"111","author":"C Zhang","year":"2025","unstructured":"Zhang, C., Zhang, Q., Zhong, W.S., Du, M.-M., Shen, S.-T., Li, X.-Y., Zhang, A.-L., Zhou, L., Sheng, Y.-B.: Memory-assisted measurement-device-independent quantum secret sharing. Phys. Rev. A 111(1), 012602 (2025)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"5183_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.110.042403","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":"5183_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.111.012603","volume":"111","author":"Q Zhang","year":"2025","unstructured":"Zhang, Q., Ying, J.-W., Wang, Z.-J., Zhong, W., Du, M.-M., Shen, S.-T., Li, X.-Y., Zhang, A.-L., Gu, S.-P., Wang, X.-F., et al.: Device-independent quantum secret sharing with advanced random key generation basis. Phys. Rev. A 111(1), 012603 (2025)","journal-title":"Phys. Rev. A"},{"key":"5183_CR22","doi-asserted-by":"crossref","unstructured":"Zhang, Q., Ying, J.-W., Gu, S.-P., Wang, X.-F., Du, M.-M., Zhong, W., Zhou, L., Sheng, Y.-B.: High-efficiency and long-distance quantum memory-assisted device-independent quantum secret sharing with single photon sources. arXiv preprint arXiv:2510.12288 (2025)","DOI":"10.1063\/5.0307766"},{"issue":"16","key":"5183_CR23","doi-asserted-by":"publisher","first-page":"5033","DOI":"10.1364\/OL.560408","volume":"50","author":"W-D Zhang","year":"2025","unstructured":"Zhang, W.-D., Nie, Z.-H., Ying, J.-W., Zhou, L., Ma, Y., Wei, H., Sheng, Y.-B.: The glare blinding attack strategy in quantum secret sharing system. Opt. Lett. 50(16), 5033\u20135036 (2025)","journal-title":"Opt. Lett."},{"issue":"4","key":"5183_CR24","doi-asserted-by":"publisher","first-page":"1202","DOI":"10.1007\/s10773-019-04012-y","volume":"58","author":"W-F Cao","year":"2019","unstructured":"Cao, W.-F., Yang, Y.-G.: Verifiable quantum secret sharing protocols based on four-qubit entangled states. Int. J. Theor. Phys. 58(4), 1202\u20131214 (2019)","journal-title":"Int. J. Theor. Phys."},{"issue":"1","key":"5183_CR25","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/s11128-019-2509-x","volume":"19","author":"C Lu","year":"2020","unstructured":"Lu, C., Miao, F., Hou, J., Huang, W., Xiong, Y.: A verifiable framework of entanglement-free quantum secret sharing with information-theoretical security. Quantum Inf. Process. 19(1), 24 (2020)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"5183_CR26","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1007\/s11433-008-0034-5","volume":"51","author":"Y Yang","year":"2008","unstructured":"Yang, Y., Wen, Q., Zhang, X.: Multiparty simultaneous quantum identity authentication with secret sharing. Sci. China, Ser. G 51(3), 321\u2013327 (2008)","journal-title":"Sci. China, Ser. G"},{"issue":"04","key":"5183_CR27","doi-asserted-by":"publisher","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(04), 1750023 (2017)","journal-title":"Int. J. Quantum Inf."},{"issue":"1","key":"5183_CR28","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/s11128-012-0380-0","volume":"12","author":"J-L Hsu","year":"2013","unstructured":"Hsu, J.-L., Chong, S.-K., Hwang, T., Tsai, C.-W.: Dynamic quantum secret sharing. Quantum Inf. Process. 12(1), 331\u2013344 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"5183_CR29","doi-asserted-by":"publisher","first-page":"1991","DOI":"10.1007\/s11128-012-0508-2","volume":"12","author":"T-Y Wang","year":"2013","unstructured":"Wang, T.-Y., Li, Y.-P.: Cryptanalysis of dynamic quantum secret sharing. Quantum Inf. Process. 12(5), 1991\u20131997 (2013)","journal-title":"Quantum Inf. Process."},{"issue":"8","key":"5183_CR30","doi-asserted-by":"publisher","DOI":"10.1088\/1674-1056\/27\/8\/080304","volume":"27","author":"Y-T Du","year":"2018","unstructured":"Du, Y.-T., Bao, W.-S.: Dynamic quantum secret sharing protocol based on two-particle transform of bell states. Chin. Phys. B 27(8), 080304 (2018)","journal-title":"Chin. Phys. B"},{"issue":"7","key":"5183_CR31","doi-asserted-by":"publisher","first-page":"2400116","DOI":"10.1002\/qute.202400116","volume":"7","author":"Y Tian","year":"2024","unstructured":"Tian, Y., Wang, J., Bian, G., Chang, J., Li, J.: Dynamic multi-party to multi-party quantum secret sharing based on bell states. Adv. Quantum Technol. 7(7), 2400116 (2024)","journal-title":"Adv. Quantum Technol."},{"issue":"5","key":"5183_CR32","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1007\/s11128-020-02662-0","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(5), 162 (2020)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"5183_CR33","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1007\/s10773-022-05081-2","volume":"61","author":"Y Xu","year":"2022","unstructured":"Xu, Y., Li, Z., Liu, T., Zhu, H.: Multi-party quantum secret sharing protocol based on GHZ states entanglement swapping. Int. J. Theor. Phys. 61(3), 76 (2022)","journal-title":"Int. J. Theor. Phys."},{"issue":"11","key":"5183_CR34","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s11128-025-04954-9","volume":"24","author":"J Li","year":"2025","unstructured":"Li, J., Chen, W., Wang, X.: An efficient and verifiable quantum secret sharing scheme based on a novel seven-qubit entangled state. Quantum Inf. Process. 24(11), 359 (2025)","journal-title":"Quantum Inf. Process."},{"issue":"10","key":"5183_CR35","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1007\/s11128-024-04535-2","volume":"23","author":"D Rathi","year":"2024","unstructured":"Rathi, D., Kumar, S.: Verifiable dynamic quantum secret sharing based on generalized Hadamard gate. Quantum Inf. Process. 23(10), 328 (2024)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"5183_CR36","doi-asserted-by":"publisher","first-page":"126","DOI":"10.1007\/s11128-025-04740-7","volume":"24","author":"Y Chen","year":"2025","unstructured":"Chen, Y., Li, S., Li, J., Zhang, J.: Multi-party dynamic secret sharing protocol based on orthogonal product states. Quantum Inf. Process. 24(5), 126 (2025)","journal-title":"Quantum Inf. Process."},{"issue":"3","key":"5183_CR37","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.92.032313","volume":"92","author":"Y-L Wang","year":"2015","unstructured":"Wang, Y.-L., Li, M.-S., Zheng, Z.J., Fei, S.-M.: Nonlocality of orthogonal product-basis quantum states. Phys. Rev. A 92(3), 032313 (2015)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"5183_CR38","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.122.040403","volume":"122","author":"S Halder","year":"2019","unstructured":"Halder, S., Banik, M., Agrawal, S., Bandyopadhyay, S.: Strong quantum nonlocality without entanglement. Phys. Rev. Lett. 122(4), 040403 (2019)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"5183_CR39","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.102.042228","volume":"102","author":"P Yuan","year":"2020","unstructured":"Yuan, P., Tian, G., Sun, X.: Strong quantum nonlocality without entanglement in multipartite quantum systems. Phys. Rev. A 102(4), 042228 (2020)","journal-title":"Phys. Rev. A"},{"issue":"3","key":"5183_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.93.032341","volume":"93","author":"G-B Xu","year":"2016","unstructured":"Xu, G.-B., Wen, Q.-Y., Qin, S.-J., Yang, Y.-H., Gao, F.: Quantum nonlocality of multipartite orthogonal product states. Phys. Rev. A 93(3), 032341 (2016)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"5183_CR41","doi-asserted-by":"publisher","first-page":"1019","DOI":"10.1088\/0253-6102\/54\/6\/13","volume":"54","author":"H Chao-Ren","year":"2010","unstructured":"Chao-Ren, H., Tzonelih, H.: Quantum secret sharing using GHZ-like state. Commun. Theor. Phys. 54(6), 1019\u20131022 (2010)","journal-title":"Commun. Theor. Phys."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05183-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-026-05183-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-026-05183-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T10:49:48Z","timestamp":1784285388000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-026-05183-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,18]]},"references-count":41,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2026,6]]}},"alternative-id":["5183"],"URL":"https:\/\/doi.org\/10.1007\/s11128-026-05183-4","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,18]]},"assertion":[{"value":"26 January 2026","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 April 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 May 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","label":"Conflict of interest","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":2,"name":"Ethics","label":"Ethical approval","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Not applicable.","order":3,"name":"Ethics","label":"Consent for publication","group":{"name":"EthicsHeading","label":"Declarations"}}],"article-number":"173"}}