{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T16:28:22Z","timestamp":1761841702749,"version":"3.37.3"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,5,1]],"date-time":"2022-05-01T00:00:00Z","timestamp":1651363200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,5,1]],"date-time":"2022-05-01T00:00:00Z","timestamp":1651363200000},"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":["61872390","61972418"],"award-info":[{"award-number":["61872390","61972418"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100010083","name":"Hunan Provincial Innovation Foundation for Postgraduate","doi-asserted-by":"publisher","award":["CX20210250"],"award-info":[{"award-number":["CX20210250"]}],"id":[{"id":"10.13039\/501100010083","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Fundamental Research Funds for the Central Universities of Central South University","award":["2021zzts0202"],"award-info":[{"award-number":["2021zzts0202"]}]},{"name":"Outstanding Youth Program of Education Department of Hunan","award":["21B0228"],"award-info":[{"award-number":["21B0228"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Quantum Inf Process"],"published-print":{"date-parts":[[2022,5]]},"DOI":"10.1007\/s11128-022-03533-6","type":"journal-article","created":{"date-parts":[[2022,5,23]],"date-time":"2022-05-23T05:03:35Z","timestamp":1653282215000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Monte Carlo-based security analysis for multi-mode continuous-variable quantum key distribution over underwater channel"],"prefix":"10.1007","volume":"21","author":[{"given":"Wei","family":"Zhao","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronghua","family":"Shi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinchao","family":"Ruan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ying","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yiyu","family":"Mao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9909-5510","authenticated-orcid":false,"given":"Yanyan","family":"Feng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,5,23]]},"reference":[{"key":"3533_CR1","doi-asserted-by":"publisher","first-page":"595","DOI":"10.1038\/nphoton.2014.149","volume":"8","author":"HK Lo","year":"2015","unstructured":"Lo, H.K., Curty, M., Tamaki, K.: Secure quantum key distribution. Nat. Photonics 8, 595\u2013604 (2015)","journal-title":"Nat. Photonics"},{"key":"3533_CR2","doi-asserted-by":"publisher","first-page":"1301","DOI":"10.1103\/RevModPhys.81.1301","volume":"81","author":"V Scarani","year":"2009","unstructured":"Scarani, V., Bechmann-Pasquinucci, H., Cerf, N.J., Du\u0161ek, M., L\u00fctkenhaus, N., Peev, M.: The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009)","journal-title":"Rev. Mod. Phys."},{"key":"3533_CR3","doi-asserted-by":"publisher","first-page":"12282","DOI":"10.1364\/OE.25.012282","volume":"25","author":"A Pomerene","year":"2017","unstructured":"Pomerene, A., Starbuck, A.L., Lentine, A.L., Long, C.M., Derose, C.T., Trotter, D.C.: Silicon photonic transceiver circuit for high-speed polarization-based discrete variable quantum key distribution. Opt. Express 25, 12282 (2017)","journal-title":"Opt. Express"},{"key":"3533_CR4","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, 441\u2013444 (2000)","journal-title":"Phys. Rev. Lett."},{"key":"3533_CR5","first-page":"1","volume":"9","author":"G Zhang","year":"2019","unstructured":"Zhang, G., Haw, J.Y., Cai, H., Xu, F., Assad, S.M., Fitzsimons, J.F., Zhou, X., Zhang, Y., Yu, S., Wu, J., Ser, W., Kwek, L.C., Liu, A.Q.: An integrated silicon photonic chip platform for continuous-variable quantum key distribution. Nat. Photonics 9, 1\u20134 (2019)","journal-title":"Nat. Photonics"},{"key":"3533_CR6","doi-asserted-by":"publisher","first-page":"052323","DOI":"10.1103\/PhysRevA.76.052323","volume":"76","author":"B Qi","year":"2007","unstructured":"Qi, B., Huang, L.L., Qian, L., Lo, H.K.: Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers. Phys. Rev. A 76, 052323 (2007)","journal-title":"Phys. Rev. A"},{"key":"3533_CR7","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1038\/nphoton.2015.83","volume":"9","author":"S Pirandola","year":"2015","unstructured":"Pirandola, S., Ottaviani, C., Spedalieri, G., Weedbrook, C., Braunstein, S.L., Lloyd, S.L., Andersen, U.L.: High-rate measurement-device-independent quantum cryptography. Nat. Photonics 9, 397\u2013402 (2015)","journal-title":"Nat. Photonics"},{"key":"3533_CR8","doi-asserted-by":"publisher","first-page":"621","DOI":"10.1103\/RevModPhys.84.621","volume":"84","author":"C Weedbrook","year":"2012","unstructured":"Weedbrook, C., Pirandola, S., Garc\u00e1-Patr\u00f3n, R., Cerf, N.J., Ralph, T.C., Shapiro, J.H., Lloyd, S.: Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)","journal-title":"Rev. Mod. Phys."},{"key":"3533_CR9","doi-asserted-by":"publisher","first-page":"057902","DOI":"10.1103\/PhysRevLett.88.057902","volume":"88","author":"F Grosshans","year":"2002","unstructured":"Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)","journal-title":"Phys. Rev. Lett."},{"key":"3533_CR10","doi-asserted-by":"publisher","first-page":"19201","DOI":"10.1038\/srep19201","volume":"6","author":"D Huang","year":"2016","unstructured":"Huang, D., Huang, P., Lin, D.K., Zeng, G.H.: Long-distance continuous-variable quantum key distribution by controlling excess noise. Sci. Rep. 6, 19201 (2016)","journal-title":"Sci. Rep."},{"key":"3533_CR11","doi-asserted-by":"publisher","first-page":"050303","DOI":"10.1103\/PhysRevA.72.050303","volume":"72","author":"J Lodewyck","year":"2005","unstructured":"Lodewyck, J., Debuisschert, T., Tualle-Brouri, R., Grangier, P.: Controlling excess noise in fiber-optics continuous-variable quantum key distribution. Phys. Rev. A 72, 050303 (2005)","journal-title":"Phys. Rev. A"},{"key":"3533_CR12","doi-asserted-by":"publisher","first-page":"31106","DOI":"10.1364\/OE.26.031106","volume":"26","author":"VC Usenko","year":"2018","unstructured":"Usenko, V.C., Peuntinger, C., Heim, B., Gunthner, K., Derkach, I., Elser, D., Marquardt, C., Filip, R., Leuchs, G.: Stabilization of transmittance fluctuations caused by beam wandering in continuous-variable quantum communication over free-space atmospheric channels. Opt. Express 26, 31106\u201331115 (2018)","journal-title":"Opt. Express"},{"key":"3533_CR13","doi-asserted-by":"publisher","first-page":"881","DOI":"10.1109\/COMST.2018.2864557","volume":"21","author":"N Hosseinidehaj","year":"2019","unstructured":"Hosseinidehaj, N., Babar, Z., Malaney, R., Ng, S.X., Hanzo, L.: Satellite-based continuous-variable quantum communications: State-of-the-art and a predictive outlook. IEEE Commun. Surv. Tutor. 21, 881\u2013919 (2019)","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"3533_CR14","first-page":"973911","volume":"9739","author":"AD Hill","year":"2016","unstructured":"Hill, A.D., Christensen, B., Kwiat, P.G.: Advanced techniques for free-space optical quantum cryptography over water. SPIE 9739, 973911 (2016)","journal-title":"SPIE"},{"key":"3533_CR15","doi-asserted-by":"publisher","first-page":"349","DOI":"10.1364\/JOSAA.32.000349","volume":"32","author":"P Shi","year":"2015","unstructured":"Shi, P., Zhao, S.C., Gu, Y.J., Li, W.D.: Channel analysis for single photon underwater free space quantum key distribution. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 32, 349\u2013356 (2015)","journal-title":"J. Opt. Soc. Am. A Opt. Image Sci. Vis."},{"key":"3533_CR16","doi-asserted-by":"publisher","first-page":"220","DOI":"10.1016\/j.optcom.2019.07.037","volume":"452","author":"DD Li","year":"2019","unstructured":"Li, D.D., Shen, Q., Chen, W., Li, Y., Han, X., Yang, K.X., Xu, Y., Lin, J., Wang, C.Z., Yong, H.L., et al.: Proof-of-principle demonstration of quantum key distribution with seawater channel: Towards space-to-underwater quantum communication. Opt. Commun. 452, 220\u2013226 (2019)","journal-title":"Opt. Commun."},{"key":"3533_CR17","doi-asserted-by":"publisher","first-page":"19795","DOI":"10.1364\/OE.25.019795","volume":"25","author":"L Ji","year":"2017","unstructured":"Ji, L., Gao, J., Yang, A.L., Feng, Z., Lin, X.F., Li, Z.G., Jin, X.M.: Towards quantum communications in free-space seawater. Opt. Express 25, 19795\u201319806 (2017)","journal-title":"Opt. Express"},{"key":"3533_CR18","doi-asserted-by":"publisher","first-page":"4956","DOI":"10.3390\/app9224956","volume":"9","author":"XC Ruan","year":"2019","unstructured":"Ruan, X.C., Zhang, H., Zhao, W., Wang, X., Li, X., Guo, Y.: Security analysis of discrete-modulated continuous-variable quantum key distribution over seawater channel. Appl. Sci. 9, 4956 (2019)","journal-title":"Appl. Sci."},{"key":"3533_CR19","doi-asserted-by":"publisher","first-page":"052326","DOI":"10.1103\/PhysRevA.97.052326","volume":"97","author":"Y Guo","year":"2018","unstructured":"Guo, Y., Xie, C.L., Huang, P., Li, J., Zhang, L., Huang, D., Zeng, G.H.: Channel-parameter estimation for satellite-to-submarine continuous-variable quantum key distribution. Phys. Rev. A 97, 052326 (2018)","journal-title":"Phys. Rev. A"},{"key":"3533_CR20","doi-asserted-by":"publisher","first-page":"5744","DOI":"10.3390\/app10175744","volume":"10","author":"Y Mao","year":"2020","unstructured":"Mao, Y., Wu, X., Huang, W., Liao, Q., Guo, Y.: Monte Carlo-based performance analysis for underwater continuous-variable quantum key distribution. Appl. Sci. 10, 5744 (2020)","journal-title":"Appl. Sci."},{"issue":"2","key":"3533_CR21","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1002\/que2.40","volume":"2","author":"MJ He","year":"2020","unstructured":"He, M.J., Malaney, R., Green, J.: Multimode CV-QKD with non-gaussian operations. Quantum Eng. 2(2), 40 (2020)","journal-title":"Quantum Eng."},{"key":"3533_CR22","doi-asserted-by":"publisher","first-page":"062326","DOI":"10.1103\/PhysRevA.90.062326","volume":"90","author":"VC Usenko","year":"2014","unstructured":"Usenko, V.C., Ruppert, L., Filip, R.: Entanglement-based CV-QKD with multimode states and detectors. Phys. Rev. A 90, 062326 (2014)","journal-title":"Phys. Rev. A"},{"key":"3533_CR23","doi-asserted-by":"publisher","first-page":"083007","DOI":"10.1088\/1367-2630\/14\/8\/083007","volume":"14","author":"A Christ","year":"2012","unstructured":"Christ, A., Lupo, C., Silberhorn, C.: Exponentially enhanced quantum communication rate by multiplexing continuous-variable teleportation. New J. Phys. 14, 083007 (2012)","journal-title":"New J. Phys."},{"key":"3533_CR24","doi-asserted-by":"publisher","first-page":"012317","DOI":"10.1103\/PhysRevA.87.012317","volume":"87","author":"P Huang","year":"2013","unstructured":"Huang, P., He, G.Q., Fang, J., Zeng, G.H.: Performance improvement of continuous-variable quantum key distribution via photon subtraction. Phys. Rev. A 87, 012317 (2013)","journal-title":"Phys. Rev. A"},{"key":"3533_CR25","doi-asserted-by":"publisher","first-page":"022315","DOI":"10.1103\/PhysRevA.80.022315","volume":"80","author":"Y Yang","year":"2009","unstructured":"Yang, Y., Li, F.L.: Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement. Phys. Rev. A 80, 022315 (2009)","journal-title":"Phys. Rev. A"},{"key":"3533_CR26","doi-asserted-by":"publisher","first-page":"043805","DOI":"10.1103\/PhysRevA.71.043805","volume":"71","author":"MS Kim","year":"2005","unstructured":"Kim, M.S., Park, E., Knight, P.L., Jeong, H.: Non classicality of a photon-subtracted Gaussian field. Phys. Rev. A 71, 043805 (2005)","journal-title":"Phys. Rev. A"},{"key":"3533_CR27","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1109\/COMST.2016.2618841","volume":"19","author":"Z Zeng","year":"2016","unstructured":"Zeng, Z., Fu, S., Zhang, H., Dong, Y., Cheng, J.: A survey of underwater optical wireless communications. IEEE Commun. Surv. Tutor. 19, 204\u2013238 (2016)","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"3533_CR28","series-title":"Wireless Mesh networks-security, architectures and protocols,","volume-title":"Monte Carlo radiative transfer modeling of underwater channel","author":"RM Kraemer","year":"2019","unstructured":"Kraemer, R.M., Pessoa, L.M., Salgado, H.M.: Monte Carlo radiative transfer modeling of underwater channel. Wireless Mesh networks-security, architectures and protocols, IntechOpen, London (2019)"},{"key":"3533_CR29","doi-asserted-by":"publisher","first-page":"21509","DOI":"10.1364\/OE.25.021509","volume":"25","author":"MW Kong","year":"2017","unstructured":"Kong, M.W., Wang, J.L., Chen, Y.F., Ali, T., Sarwar, R., Qiu, Y., Wang, S.L., Han, J., Xu, J.: Security weaknesses of underwater wireless optical communication. Opt. Express 25, 21509\u201321518 (2017)","journal-title":"Opt. Express"},{"key":"3533_CR30","doi-asserted-by":"publisher","first-page":"066001","DOI":"10.1117\/1.OE.51.6.066001","volume":"51","author":"J Li","year":"2012","unstructured":"Li, J., Ma, Y., Zhou, Q.Q., Zhou, B., Wang, H.Y.: Monte Carlo study on pulse response of underwater optical channel. Opt. Eng. 51, 066001 (2012)","journal-title":"Opt. Eng."},{"key":"3533_CR31","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1364\/JOCN.5.000001","volume":"5","author":"C Gabriel","year":"2013","unstructured":"Gabriel, C., Khalighi, M.A., Bourennane, S., L\u00e9on, P., Rigaud, V.: Monte-Carlo-Based channel characterization for underwater optical communication systems. J. Opt. Commun. Netw. 5, 1\u201312 (2013)","journal-title":"J. Opt. Commun. Netw."},{"key":"3533_CR32","unstructured":"Cox, W.C.: Simulation, modeling, and design of underwater optical communication systems. Ph. D. Thesis, North Carolina State University, Raleigh, NC (2012)"},{"key":"3533_CR33","doi-asserted-by":"crossref","unstructured":"He, M., Malaney, R., Barnett, B.: Multi-mode CV-QKD with noiseless attenuation and amplification, arXiv:2006.02094 (2020)","DOI":"10.1109\/GCWkshps50303.2020.9367581"}],"container-title":["Quantum Information Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03533-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11128-022-03533-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11128-022-03533-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,8]],"date-time":"2022-06-08T08:31:34Z","timestamp":1654677094000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11128-022-03533-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,5]]},"references-count":33,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,5]]}},"alternative-id":["3533"],"URL":"https:\/\/doi.org\/10.1007\/s11128-022-03533-6","relation":{},"ISSN":["1573-1332"],"issn-type":[{"type":"electronic","value":"1573-1332"}],"subject":[],"published":{"date-parts":[[2022,5]]},"assertion":[{"value":"28 August 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 May 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"186"}}