{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T03:16:14Z","timestamp":1773717374172,"version":"3.50.1"},"reference-count":38,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,1]],"date-time":"2021-04-01T00:00:00Z","timestamp":1617235200000},"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":["61902132"],"award-info":[{"award-number":["61902132"]}],"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":["11647140"],"award-info":[{"award-number":["11647140"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Natural Science Foundation of Guangdong Province of China","award":["2018A030310147"],"award-info":[{"award-number":["2018A030310147"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["U1736113"],"award-info":[{"award-number":["U1736113"]}],"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"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s11128-021-03072-6","type":"journal-article","created":{"date-parts":[[2021,4,9]],"date-time":"2021-04-09T06:03:39Z","timestamp":1617948219000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Quantum summation using d-level entanglement swapping"],"prefix":"10.1007","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8388-9006","authenticated-orcid":false,"given":"Cai","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yinxiang","family":"Long","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qin","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,9]]},"reference":[{"issue":"1","key":"3072_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jcom.2001.0629","volume":"18","author":"S Heinrich","year":"2002","unstructured":"Heinrich, S.: Quantum summation with an application to integration. J. Complex. 18(1), 1 (2002)","journal-title":"J. Complex."},{"issue":"1","key":"3072_CR2","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0885-064X(02)00003-1","volume":"19","author":"S Heinrich","year":"2003","unstructured":"Heinrich, S., Novak, E.: On a problem in quantum summation. J. Complex. 19(1), 1 (2003)","journal-title":"J. Complex."},{"key":"3072_CR3","doi-asserted-by":"crossref","unstructured":"Heinrich, S., Kwas, H., Wozniakowski, M.: Quantum Boolean Summation with Repetitions in the Worst-Average Setting (2003). arXiv:quant-ph\/0311036","DOI":"10.1007\/978-3-642-18743-8_14"},{"issue":"11","key":"3072_CR4","doi-asserted-by":"crossref","first-page":"6214","DOI":"10.7498\/aps.56.6214","volume":"56","author":"JZ Du","year":"2007","unstructured":"Du, J.Z., Chen, X.B., Wen, Q.Y., Zhu, F.C.: Secure multiparty quantum summation. Acta Phys. Sin. 56(11), 6214 (2007)","journal-title":"Acta Phys. Sin."},{"issue":"11","key":"3072_CR5","doi-asserted-by":"publisher","first-page":"2793","DOI":"10.1007\/s10773-010-0472-5","volume":"49","author":"XB Chen","year":"2010","unstructured":"Chen, X.B., Xu, G., Yang, Y.X., Wen, Q.Y.: An efficient protocol for the secure multi-party quantum summation. Int. J. Theor. Phys. 49(11), 2793 (2010)","journal-title":"Int. J. Theor. Phys."},{"key":"3072_CR6","doi-asserted-by":"publisher","first-page":"1154","DOI":"10.1103\/PhysRevA.56.1154","volume":"56","author":"HK Lo","year":"1997","unstructured":"Lo, H.K.: Insecurity of quantum secure computations. Phys. Rev. A 56, 1154 (1997)","journal-title":"Phys. Rev. A"},{"key":"3072_CR7","doi-asserted-by":"crossref","unstructured":"Cr\u00e9peau, C., Gottesman, D., Smith, A.: Secure multi-party quantum computation. In: Proceedings of the Thirty-Fourth Annual ACM Symposium on Theory of Computing, pp. 643\u2013652. ACM (2002)","DOI":"10.1145\/509907.510000"},{"key":"3072_CR8","doi-asserted-by":"publisher","first-page":"032308","DOI":"10.1103\/PhysRevA.61.032308","volume":"61","author":"HF Chau","year":"2000","unstructured":"Chau, H.F.: Quantum-classical complexity\u2013security tradeoff in secure multiparty computations. Phys. Rev. A 61, 032308 (2000)","journal-title":"Phys. Rev. A"},{"key":"3072_CR9","doi-asserted-by":"crossref","unstructured":"Ben-Or, M., Crepeau, C., Gottesman, D., Hassidim, A., Smith, A.: Secure multiparty quantum computation with (only) a strict honest majority. In: 47th Annual IEEE Symposium on Foundations of Computer Science, 2006. FOCS\u201906, pp. 249\u2013260. IEEE (2006)","DOI":"10.1109\/FOCS.2006.68"},{"key":"3072_CR10","unstructured":"Smith, A.: Multi-party Quantum Computation (2010). arXiv:quant-ph\/0111030"},{"issue":"1\u20134","key":"3072_CR11","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/j.physleta.2005.09.010","volume":"349","author":"M Hillery","year":"2006","unstructured":"Hillery, M., Ziman, M., Bu\u017eek, V., Bielikov\u00e1, M.: Towards quantum-based privacy and voting. Phys. Lett. A 349(1\u20134), 75 (2006)","journal-title":"Phys. Lett. A"},{"issue":"5","key":"3072_CR12","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1007\/s10043-008-0034-8","volume":"15","author":"Y Li","year":"2008","unstructured":"Li, Y., Zeng, G.: Quantum anonymous voting systems based on entangled state. Opt. Rev. 15(5), 219 (2008)","journal-title":"Opt. Rev."},{"issue":"2","key":"3072_CR13","doi-asserted-by":"publisher","first-page":"022333","DOI":"10.1103\/PhysRevA.94.022333","volume":"94","author":"Q Wang","year":"2016","unstructured":"Wang, Q., Yu, C., Gao, F., Qi, H., Wen, Q.: Self-tallying quantum anonymous voting. Phys. Rev. A 94(2), 022333 (2016)","journal-title":"Phys. Rev. A"},{"issue":"1","key":"3072_CR14","doi-asserted-by":"publisher","first-page":"7586","DOI":"10.1038\/s41598-017-07976-1","volume":"7","author":"P Xue","year":"2017","unstructured":"Xue, P., Zhang, X.: A simple quantum voting scheme with multi-qubit entanglement. Sci. Rep. 7(1), 7586 (2017)","journal-title":"Sci. Rep."},{"key":"3072_CR15","doi-asserted-by":"crossref","unstructured":"Bao, N., Halpern, N.Y.: Quantum voting and violation of Arrow\u2019s impossibility theorem. Phys. Rev. A 95(6), 062306 (2017)","DOI":"10.1103\/PhysRevA.95.062306"},{"issue":"3","key":"3072_CR16","doi-asserted-by":"publisher","first-page":"032325","DOI":"10.1103\/PhysRevA.89.032325","volume":"89","author":"W Huang","year":"2014","unstructured":"Huang, W., Wen, Q.Y., Liu, B., Su, Q., Qin, S.J., Gao, F.: Quantum anonymous ranking. Phys. Rev. A 89(3), 032325 (2014)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"3072_CR17","doi-asserted-by":"publisher","first-page":"2125","DOI":"10.1007\/s11128-015-0956-6","volume":"14","author":"Z Sun","year":"2015","unstructured":"Sun, Z., Yu, J., Wang, P., Xu, L., Wu, C.: Quantum private comparison with a malicious third party. Quantum Inf. Process. 14(6), 2125 (2015)","journal-title":"Quantum Inf. Process."},{"issue":"2","key":"3072_CR18","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s11128-016-1498-2","volume":"16","author":"SM Hung","year":"2017","unstructured":"Hung, S.M., Hwang, S.L., Hwang, T., Kao, S.H.: Multiparty quantum private comparison with almost dishonest third parties for strangers. Quantum Inf. Process. 16(2), 36 (2017)","journal-title":"Quantum Inf. Process."},{"issue":"02","key":"3072_CR19","doi-asserted-by":"publisher","first-page":"1750014","DOI":"10.1142\/S0219749917500149","volume":"15","author":"GP He","year":"2017","unstructured":"He, G.P.: Quantum private comparison protocol without a third party. Int. J. Quantum Inf. 15(02), 1750014 (2017)","journal-title":"Int. J. Quantum Inf."},{"issue":"3","key":"3072_CR20","doi-asserted-by":"publisher","first-page":"933","DOI":"10.1007\/s10773-013-1884-9","volume":"53","author":"C Zhang","year":"2014","unstructured":"Zhang, C., Sun, Z., Huang, Y., Long, D.: High-capacity quantum summation with single photons in both polarization and spatial-mode degrees of freedom. Int. J. Theor. Phys. 53(3), 933 (2014)","journal-title":"Int. J. Theor. Phys."},{"issue":"02","key":"3072_CR21","doi-asserted-by":"publisher","first-page":"1550011","DOI":"10.1142\/S0219749915500112","volume":"13","author":"C Zhang","year":"2015","unstructured":"Zhang, C., Sun, Z.W., Huang, X., Long, D.Y.: Three-party quantum summation without a trusted third party. Int. J. Quantum Inf. 13(02), 1550011 (2015)","journal-title":"Int. J. Quantum Inf."},{"key":"3072_CR22","doi-asserted-by":"publisher","first-page":"19655","DOI":"10.1038\/srep19655","volume":"6","author":"RH Shi","year":"2016","unstructured":"Shi, R.H., Mu, Y., Zhong, H., Cui, J., Zhang, S.: Secure multiparty quantum computation for summation and multiplication. Sci. Rep. 6, 19655 (2016)","journal-title":"Sci. Rep."},{"issue":"9","key":"3072_CR23","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/s11128-017-1676-x","volume":"16","author":"RH Shi","year":"2017","unstructured":"Shi, R.H., Zhang, S.: Quantum solution to a class of two-party private summation problems. Quantum Inf. Process. 16(9), 225 (2017)","journal-title":"Quantum Inf. Process."},{"key":"3072_CR24","doi-asserted-by":"publisher","first-page":"1750010","DOI":"10.1142\/S0219749917500101","volume":"15","author":"C Zhang","year":"2017","unstructured":"Zhang, C., Situ, H., Huang, Q., Yang, P.: Multi-party quantum summation without a trusted third party based on single particles. Int. J. Quantum Inf. 15, 1750010 (2017)","journal-title":"Int. J. Quantum Inf."},{"issue":"9","key":"3072_CR25","doi-asserted-by":"publisher","first-page":"2783","DOI":"10.1007\/s10773-017-3442-3","volume":"56","author":"W Liu","year":"2017","unstructured":"Liu, W., Wang, Y.B., Fan, W.Q.: An novel protocol for the quantum secure multi-party summation based on two-particle bell states. Int. J. Theor. Phys. 56(9), 2783 (2017)","journal-title":"Int. J. Theor. Phys."},{"key":"3072_CR26","doi-asserted-by":"publisher","first-page":"044302","DOI":"10.1103\/PhysRevA.72.044302","volume":"72","author":"FG Deng","year":"2005","unstructured":"Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72, 044302 (2005)","journal-title":"Phys. Rev. A"},{"key":"3072_CR27","doi-asserted-by":"publisher","first-page":"022320","DOI":"10.1103\/PhysRevA.73.022320","volume":"73","author":"N Gisin","year":"2006","unstructured":"Gisin, N., Fasel, S., Kraus, B., Zbinden, H., Ribordy, G.: Trojan-horse attacks on quantum-key-distribution systems. Phys. Rev. A 73, 022320 (2006)","journal-title":"Phys. Rev. A"},{"key":"3072_CR28","doi-asserted-by":"publisher","first-page":"054302","DOI":"10.1103\/PhysRevA.74.054302","volume":"74","author":"XH Li","year":"2006","unstructured":"Li, X.H., Deng, F.G., Zhou, H.Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A 74, 054302 (2006)","journal-title":"Phys. Rev. A"},{"issue":"7","key":"3072_CR29","doi-asserted-by":"publisher","first-page":"719","DOI":"10.3390\/e21070719","volume":"21","author":"C Zhang","year":"2019","unstructured":"Zhang, C., Razavi, M., Sun, Z., Huang, Q., Situ, H.: Multi-party quantum summation based on quantum teleportation. Entropy 21(7), 719 (2019)","journal-title":"Entropy"},{"issue":"6","key":"3072_CR30","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1007\/s11128-018-2141-1","volume":"18","author":"Z Ji","year":"2019","unstructured":"Ji, Z., Zhang, H., Wang, H., Wu, F., Jia, J., Wu, W.: Quantum protocols for secure multi-party summation. Quantum Inf. Process. 18(6), 168 (2019)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"3072_CR31","doi-asserted-by":"publisher","first-page":"042320","DOI":"10.1103\/PhysRevA.65.042320","volume":"65","author":"V Karimipour","year":"2002","unstructured":"Karimipour, V., Bahraminasab, A., Bagherinezhad, S.: Entanglement swapping of generalized cat states and secret sharing. Phys. Rev. A 65(4), 042320 (2002)","journal-title":"Phys. Rev. A"},{"issue":"4","key":"3072_CR32","first-page":"4","volume":"72","author":"FG Deng","year":"2005","unstructured":"Deng, F.G., Li, X.H., Zhou, H.Y., Zhang, Z.: Improving the security of multiparty quantum secret sharing against Trojan horse attack. Phys. Rev. A 72(4), 4 (2005)","journal-title":"Phys. Rev. A"},{"issue":"02","key":"3072_CR33","doi-asserted-by":"publisher","first-page":"022320","DOI":"10.1103\/PhysRevA.73.022320","volume":"73","author":"N Gisin","year":"2006","unstructured":"Gisin, N., Fasel, S., Kraus, B., Zbinden, H., Ribordy, G.: Trojan-horse attacks on quantum-key-distribution systems. Phys. Rev. A 73(02), 022320 (2006)","journal-title":"Phys. Rev. A"},{"key":"3072_CR34","unstructured":"Bennett, C.H., Brassard, G.: Quantum cryptography: public-key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computer, System and Signal, pp. 175\u2013179 (1984)"},{"issue":"2","key":"3072_CR35","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1103\/PhysRevLett.85.441","volume":"85","author":"PW Shor","year":"2000","unstructured":"Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441 (2000)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"3072_CR36","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1007\/s11128-018-1890-1","volume":"17","author":"HY Yang","year":"2018","unstructured":"Yang, H.Y., Ye, T.Y.: Secure multi-party quantum summation based on quantum Fourier transform. Quantum Inf. Process. 17(6), 129 (2018)","journal-title":"Quantum Inf. Process."},{"key":"3072_CR37","doi-asserted-by":"publisher","first-page":"1950027","DOI":"10.1142\/S0219749919500278","volume":"17","author":"C Zhang","year":"2019","unstructured":"Zhang, C., Situ, H., Huang, Q., Sun, Z., Huang, Z.: Multi-party quantum summation based on quantum teleportation. Int. J. Quantum Inf. 17, 1950027 (2019)","journal-title":"Int. J. Quantum Inf."},{"key":"3072_CR38","doi-asserted-by":"publisher","first-page":"3086","DOI":"10.1007\/s10773-020-04555-5","volume":"59","author":"ZG Gan","year":"2020","unstructured":"Gan, Z.G.: Improvement of quantum protocols for secure multi-party summation. Int. J. Theor. Phys. 59, 3086 (2020)","journal-title":"Int. J. Theor. Phys."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03072-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-021-03072-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-021-03072-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,23]],"date-time":"2022-12-23T21:36:58Z","timestamp":1671831418000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-021-03072-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4]]},"references-count":38,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["3072"],"URL":"https:\/\/doi.org\/10.1007\/s11128-021-03072-6","relation":{},"ISSN":["1570-0755","1573-1332"],"issn-type":[{"value":"1570-0755","type":"print"},{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4]]},"assertion":[{"value":"9 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 March 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 April 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"137"}}