{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T13:25:37Z","timestamp":1781616337070,"version":"3.54.5"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T00:00:00Z","timestamp":1739750400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T00:00:00Z","timestamp":1739750400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"name":"UPT innovation and entrepreneurship support program","award":["No.2024-YC-A188"],"award-info":[{"award-number":["No.2024-YC-A188"]}]},{"name":"BUPT Excellent Ph.D. Students Foundation","award":["No.CX2023207"],"award-info":[{"award-number":["No.CX2023207"]}]},{"name":"the state Key Laboratory of Information Photonics and Optical Communications","award":["No.IPOC2021ZT10"],"award-info":[{"award-number":["No.IPOC2021ZT10"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"DOI":"10.1007\/s11128-025-04681-1","type":"journal-article","created":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T07:45:51Z","timestamp":1739778351000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Twin-field quantum key distribution based on particle swarm optimization algorithm"],"prefix":"10.1007","volume":"24","author":[{"given":"Chang","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yue","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haoyang","family":"Wang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kaiyi","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"ZhongQi","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiaao","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yujia","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Duo","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haiqiang","family":"Ma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,2,17]]},"reference":[{"issue":"5886","key":"4681_CR1","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1038\/299802a0","volume":"299","author":"WK Wootters","year":"1982","unstructured":"Wootters, W.K., Zurek, W.H.: A single quantum cannot be cloned. Nature 299(5886), 802\u2013803 (1982)","journal-title":"Nature"},{"key":"4681_CR2","doi-asserted-by":"publisher","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. Theor. Comput. Sci. 560, 7\u201311 (2014)","journal-title":"Theor. Comput. Sci."},{"key":"4681_CR3","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/s11128-014-0886-8","volume":"14","author":"Y Ou-Yang","year":"2015","unstructured":"Ou-Yang, Y., Feng, Z.-F., Zhou, L., Sheng, Y.-B.: Protecting single-photon entanglement with imperfect single-photon source. Quantum Inf. Process. 14, 635\u2013651 (2015)","journal-title":"Quantum Inf. Process."},{"key":"4681_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-020-02902-3","volume":"19","author":"S-S Han","year":"2020","unstructured":"Han, S.-S., Ding, H.-J., Zhang, C.-H., Zhou, X.-Y., Zhang, C.-M., Wang, Q.: Practical decoy-state quantum random number generator with weak coherent sources. Quantum Inf. Process. 19, 1\u20139 (2020)","journal-title":"Quantum Inf. Process."},{"issue":"5","key":"4681_CR5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.91.057901","volume":"91","author":"W-Y Hwang","year":"2003","unstructured":"Hwang, W.-Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91(5), 057901 (2003)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"4681_CR6","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1088\/1367-2630\/4\/1\/344","volume":"4","author":"N L\u00fctkenhaus","year":"2002","unstructured":"L\u00fctkenhaus, N., Jahma, M.: Quantum key distribution with realistic states: photon-number statistics in the photon-number splitting attack. New J. Phys. 4(1), 44 (2002)","journal-title":"New J. Phys."},{"issue":"23","key":"4681_CR7","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.94.230504","volume":"94","author":"H-K Lo","year":"2005","unstructured":"Lo, H.-K., Ma, X., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94(23), 230504 (2005)","journal-title":"Phys. Rev. Lett."},{"issue":"7","key":"4681_CR8","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.070502","volume":"96","author":"Y Zhao","year":"2006","unstructured":"Zhao, Y., Qi, B., Ma, X., Lo, H.-K., Qian, L.: Experimental quantum key distribution with decoy states. Phys. Rev. Lett. 96(7), 070502 (2006)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"4681_CR9","doi-asserted-by":"publisher","first-page":"520","DOI":"10.1364\/OPTICA.485389","volume":"10","author":"F-Y Lu","year":"2023","unstructured":"Lu, F.-Y., Ye, P., Wang, Z.-H., Wang, S., Yin, Z.-Q., Wang, R., Huang, X.-J., Chen, W., He, D.-Y., Fan-Yuan, G.-J., et al.: Hacking measurement-device-independent quantum key distribution. Optica 10(4), 520\u2013527 (2023)","journal-title":"Optica"},{"issue":"2","key":"4681_CR10","doi-asserted-by":"publisher","first-page":"176","DOI":"10.3390\/e23020176","volume":"23","author":"Y Zheng","year":"2021","unstructured":"Zheng, Y., Shi, H., Pan, W., Wang, Q., Mao, J.: Quantum hacking on an integrated continuous-variable quantum key distribution system via power analysis. Entropy 23(2), 176 (2021)","journal-title":"Entropy"},{"issue":"13","key":"4681_CR11","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.108.130503","volume":"108","author":"H-K Lo","year":"2012","unstructured":"Lo, H.-K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108(13), 130503 (2012)","journal-title":"Phys. Rev. Lett."},{"issue":"1","key":"4681_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/ncomms15043","volume":"8","author":"S Pirandola","year":"2017","unstructured":"Pirandola, S., Laurenza, R., Ottaviani, C., Banchi, L.: Fundamental limits of repeaterless quantum communications. Nat. Commun. 8(1), 1\u201315 (2017)","journal-title":"Nat. Commun."},{"issue":"7705","key":"4681_CR13","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1038\/s41586-018-0066-6","volume":"557","author":"M Lucamarini","year":"2018","unstructured":"Lucamarini, M., Yuan, Z.L., Dynes, J.F., Shields, A.J.: Overcoming the rate-distance limit of quantum key distribution without quantum repeaters. Nature 557(7705), 400\u2013403 (2018)","journal-title":"Nature"},{"issue":"1","key":"4681_CR14","doi-asserted-by":"publisher","first-page":"3045","DOI":"10.1038\/s41598-019-39454-1","volume":"9","author":"H-L Yin","year":"2019","unstructured":"Yin, H.-L., Fu, Y.: Measurement-device-independent twin-field quantum key distribution. Sci. Rep. 9(1), 3045 (2019)","journal-title":"Sci. Rep."},{"issue":"3","key":"4681_CR15","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.94.032335","volume":"94","author":"Y Wang","year":"2016","unstructured":"Wang, Y., Bao, W.-S., Zhou, C., Jiang, M.-S., Li, H.-W.: Tight finite-key analysis of a practical decoy-state quantum key distribution with unstable sources. Phys. Rev. A 94(3), 032335 (2016)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"4681_CR16","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/ab81b7","volume":"22","author":"C Jiang","year":"2020","unstructured":"Jiang, C., Hu, X.-L., Xu, H., Yu, Z.-W., Wang, X.-B.: Zigzag approach to higher key rate of sending-or-not-sending twin field quantum key distribution with finite-key effects. New J. Phys. 22(5), 053048 (2020)","journal-title":"New J. Phys."},{"issue":"11","key":"4681_CR17","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/aaec34","volume":"20","author":"F Grasselli","year":"2018","unstructured":"Grasselli, F., Kampermann, H., Bru\u00df, D.: Finite-key effects in multipartite quantum key distribution protocols. New J. Phys. 20(11), 113014 (2018)","journal-title":"New J. Phys."},{"issue":"3","key":"4681_CR18","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1038\/nphoton.2014.327","volume":"9","author":"B Korzh","year":"2015","unstructured":"Korzh, B., Lim, C.C.W., Houlmann, R., Gisin, N., Li, M.J., Nolan, D., Sanguinetti, B., Thew, R., Zbinden, H.: Provably secure and practical quantum key distribution over 307 km of optical fibre. Nat. Photon. 9(3), 163\u2013168 (2015)","journal-title":"Nat. Photon."},{"issue":"2","key":"4681_CR19","doi-asserted-by":"publisher","first-page":"154","DOI":"10.1038\/s41566-021-00928-2","volume":"16","author":"S Wang","year":"2022","unstructured":"Wang, S., Yin, Z.-Q., He, D.-Y., Wang, R.-Q., Ye, P., Zhou, Y., Fan-Yuan, G.-J., Wang, F.-X., Chen, W., Chen, W., et al.: Twin-field quantum key distribution over 830-km fibre. Nat. Photon. 16(2), 154\u2013161 (2022)","journal-title":"Nat. Photon."},{"issue":"19","key":"4681_CR20","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.121.190502","volume":"121","author":"A Boaron","year":"2018","unstructured":"Boaron, A., Boso, G., Rusca, D., Vulliez, C., Autebert, C., Caloz, M., Perrenoud, M., Gras, G., Bussi\u00e8res, F., Li, M.-J., et al.: Secure quantum key distribution over 421 km of optical fiber. Phys. Rev. Lett. 121(19), 190502 (2018)","journal-title":"Phys. Rev. Lett."},{"issue":"19","key":"4681_CR21","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.190501","volume":"117","author":"H-L Yin","year":"2016","unstructured":"Yin, H.-L., Chen, T.-Y., Yu, Z.-W., Liu, H., You, L.-X., Zhou, Y.-H., Chen, S.-J., Mao, Y., Huang, M.-Q., Zhang, W.-J., et al.: Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117(19), 190501 (2016)","journal-title":"Phys. Rev. Lett."},{"issue":"6","key":"4681_CR22","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.98.062323","volume":"98","author":"X-B Wang","year":"2018","unstructured":"Wang, X.-B., Yu, Z.-W., Hu, X.-L.: Twin-field quantum key distribution with large misalignment error. Phys. Rev. A 98(6), 062323 (2018)","journal-title":"Phys. Rev. A"},{"issue":"5","key":"4681_CR23","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.89.052333","volume":"89","author":"F Xu","year":"2014","unstructured":"Xu, F., Xu, H., Lo, H.-K.: Protocol choice and parameter optimization in decoy-state measurement-device-independent quantum key distribution. Phys. Rev. A 89(5), 052333 (2014)","journal-title":"Phys. Rev. A"},{"issue":"6","key":"4681_CR24","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.100.062334","volume":"100","author":"W Wang","year":"2019","unstructured":"Wang, W., Lo, H.-K.: Machine learning for optimal parameter prediction in quantum key distribution. Phys. Rev. A 100(6), 062334 (2019)","journal-title":"Phys. Rev. A"},{"issue":"7","key":"4681_CR25","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s11128-022-03579-6","volume":"21","author":"Q Dong","year":"2022","unstructured":"Dong, Q., Huang, G., Cui, W., Jiao, R.: Optimization parameter prediction-based XGBoost of TF-QKD. Quantum Inf. Process. 21(7), 233 (2022)","journal-title":"Quantum Inf. Process."},{"issue":"4","key":"4681_CR26","doi-asserted-by":"publisher","first-page":"2000131","DOI":"10.1002\/qute.202000131","volume":"4","author":"G-J Fan-Yuan","year":"2021","unstructured":"Fan-Yuan, G.-J., Wang, Z.-H., Wang, S., Yin, Z.-Q., Chen, W., He, D.-Y., Guo, G.-C., Han, Z.-F.: Optimizing decoy-state protocols for practical quantum key distribution systems. Adv. Quantum Technol. 4(4), 2000131 (2021)","journal-title":"Adv. Quantum Technol."},{"issue":"6","key":"4681_CR27","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.100.062334","volume":"100","author":"W Wang","year":"2019","unstructured":"Wang, W., Lo, H.-K.: Machine learning for optimal parameter prediction in quantum key distribution. Phys. Rev. A 100(6), 062334 (2019)","journal-title":"Phys. Rev. A"},{"key":"4681_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s11128-019-2548-3","volume":"19","author":"H-J Ding","year":"2020","unstructured":"Ding, H.-J., Liu, J.-Y., Zhang, C.-M., Wang, Q.: Predicting optimal parameters with random forest for quantum key distribution. Quantum Inf. Process. 19, 1\u20138 (2020)","journal-title":"Quantum Inf. Process."},{"issue":"7","key":"4681_CR29","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s11128-022-03579-6","volume":"21","author":"Q Dong","year":"2022","unstructured":"Dong, Q., Huang, G., Cui, W., Jiao, R.: Optimization parameter prediction-based XGBoost of TF-QKD. Quantum Inf. Process. 21(7), 233 (2022)","journal-title":"Quantum Inf. Process."},{"issue":"10","key":"4681_CR30","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s11128-023-04130-x","volume":"22","author":"L Wang","year":"2023","unstructured":"Wang, L., Dong, Q., Jiao, R.: Parameter optimization in decoy-state phase-matching quantum key distribution. Quantum Inf. Process. 22(10), 373 (2023)","journal-title":"Quantum Inf. Process."},{"key":"4681_CR31","doi-asserted-by":"crossref","unstructured":"Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the 6th International Symposium on Micromachine Human Science, pp. 39\u201343 (1995)","DOI":"10.1109\/MHS.1995.494215"},{"key":"4681_CR32","doi-asserted-by":"publisher","DOI":"10.1016\/j.swevo.2020.100718","volume":"58","author":"AP Piotrowski","year":"2020","unstructured":"Piotrowski, A.P., Napiorkowski, J.J., Piotrowska, A.E.: Population size in particle swarm optimization. Swarm Evol. Comput. 58, 100718 (2020)","journal-title":"Swarm Evol. Comput."},{"key":"4681_CR33","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1016\/j.chemolab.2015.08.020","volume":"149","author":"F Marini","year":"2015","unstructured":"Marini, F., Walczak, B.: Particle swarm optimization (PSO): a tutorial. Chemometr. Intell. Lab. Syst. 149, 153\u2013165 (2015)","journal-title":"Chemometr. Intell. Lab. Syst."},{"issue":"10","key":"4681_CR34","doi-asserted-by":"publisher","first-page":"2238","DOI":"10.1109\/TCYB.2015.2474153","volume":"46","author":"Q Qin","year":"2015","unstructured":"Qin, Q., Cheng, S., Zhang, Q., Li, L., Shi, Y.: Particle swarm optimization with interswarm interactive learning strategy. IEEE Trans. Cybern. 46(10), 2238\u20132251 (2015)","journal-title":"IEEE Trans. Cybern."},{"issue":"2","key":"4681_CR35","first-page":"224","volume":"46","author":"L Rongyu","year":"2017","unstructured":"Rongyu, L., Zhiyong, Z.: Particle swarm optimization algorithm with growth property and its application in function optimization. Inf. Control 46(2), 224\u2013230 (2017)","journal-title":"Inf. Control"},{"issue":"6","key":"4681_CR36","doi-asserted-by":"publisher","first-page":"2011","DOI":"10.1109\/TCYB.2018.2817020","volume":"49","author":"J Zhang","year":"2018","unstructured":"Zhang, J., Zhu, X., Wang, Y., Zhou, M.: Dual-environmental particle swarm optimizer in noisy and noise-free environments. IEEE Trans Cybern. 49(6), 2011\u20132021 (2018)","journal-title":"IEEE Trans Cybern."},{"issue":"3","key":"4681_CR37","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1109\/TEVC.2005.857610","volume":"10","author":"JJ Liang","year":"2006","unstructured":"Liang, J.J., Qin, A.K., Suganthan, P.N., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans. Evol. 10(3), 281\u2013295 (2006)","journal-title":"IEEE Trans. Evol."},{"key":"4681_CR38","unstructured":"Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: Proceedings of the IEEE International Conference on Evolutionary Computation, pp. 69\u201373 (1998)"},{"issue":"1","key":"4681_CR39","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.012326","volume":"72","author":"X Ma","year":"2005","unstructured":"Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Practical decoy state for quantum key distribution. Phys. Rev. A Atom. Mol. Opt. Phys. 72(1), 012326 (2005)","journal-title":"Phys. Rev. A Atom. Mol. Opt. Phys."},{"issue":"1","key":"4681_CR40","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.72.012326","volume":"72","author":"X Ma","year":"2005","unstructured":"Ma, X., Qi, B., Zhao, Y., Lo, H.-K.: Practical decoy state for quantum key distribution. Phys. Rev. A: Atom. Mol. Opt. Phys. 72(1), 012326 (2005)","journal-title":"Phys. Rev. A: Atom. Mol. Opt. Phys."}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04681-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-025-04681-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-025-04681-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T04:01:42Z","timestamp":1742184102000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-025-04681-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,17]]},"references-count":40,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["4681"],"URL":"https:\/\/doi.org\/10.1007\/s11128-025-04681-1","relation":{},"ISSN":["1573-1332"],"issn-type":[{"value":"1573-1332","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,2,17]]},"assertion":[{"value":"18 March 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 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":"59"}}