{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T19:07:18Z","timestamp":1782932838716,"version":"3.54.5"},"reference-count":28,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,14]],"date-time":"2023-06-14T00:00:00Z","timestamp":1686700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"key research and development project in Hunan Province","award":["2022GK2016"],"award-info":[{"award-number":["2022GK2016"]}]},{"name":"key research and development project in Hunan Province","award":["22C0446"],"award-info":[{"award-number":["22C0446"]}]},{"name":"key research and development project in Hunan Province","award":["21A0470"],"award-info":[{"award-number":["21A0470"]}]},{"name":"key research and development project in Hunan Province","award":["22A0669"],"award-info":[{"award-number":["22A0669"]}]},{"name":"key research and development project in Hunan Province","award":["2023JJ50268"],"award-info":[{"award-number":["2023JJ50268"]}]},{"name":"key research and development project in Hunan Province","award":["2023JJ50269"],"award-info":[{"award-number":["2023JJ50269"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["2022GK2016"],"award-info":[{"award-number":["2022GK2016"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["22C0446"],"award-info":[{"award-number":["22C0446"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["21A0470"],"award-info":[{"award-number":["21A0470"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["22A0669"],"award-info":[{"award-number":["22A0669"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["2023JJ50268"],"award-info":[{"award-number":["2023JJ50268"]}]},{"name":"Scientific Research Fund of Hunan Provincial Education Department","award":["2023JJ50269"],"award-info":[{"award-number":["2023JJ50269"]}]},{"name":"Key project of Scientific Research of Hunan Provincial Education Department","award":["2022GK2016"],"award-info":[{"award-number":["2022GK2016"]}]},{"name":"Key project of Scientific Research of Hunan Provincial Education Department","award":["22C0446"],"award-info":[{"award-number":["22C0446"]}]},{"name":"Key project of Scientific Research of Hunan Provincial Education Department","award":["21A0470"],"award-info":[{"award-number":["21A0470"]}]},{"name":"Key project of Scientific Research of Hunan Provincial Education Department","award":["22A0669"],"award-info":[{"award-number":["22A0669"]}]},{"name":"Key project of Scientific Research of Hunan Provincial Education Department","award":["2023JJ50268"],"award-info":[{"award-number":["2023JJ50268"]}]},{"name":"Key project of Scientific Research of Hunan Provincial Education Department","award":["2023JJ50269"],"award-info":[{"award-number":["2023JJ50269"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["2022GK2016"],"award-info":[{"award-number":["2022GK2016"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["22C0446"],"award-info":[{"award-number":["22C0446"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["21A0470"],"award-info":[{"award-number":["21A0470"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["22A0669"],"award-info":[{"award-number":["22A0669"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["2023JJ50268"],"award-info":[{"award-number":["2023JJ50268"]}]},{"name":"Natural Science Foundation of Hunan Province","award":["2023JJ50269"],"award-info":[{"award-number":["2023JJ50269"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Continuous-variable quantum key distribution (CVQKD) plays an important role in quantum communications, because of its compatible setup for optical implementation with low cost. For this paper, we considered a neural network approach to predicting the secret key rate of CVQKD with discrete modulation (DM) through an underwater channel. A long-short-term-memory-(LSTM)-based neural network (NN) model was employed, in order to demonstrate performance improvement when taking into account the secret key rate. The numerical simulations showed that the lower bound of the secret key rate could be achieved for a finite-size analysis, where the LSTM-based neural network (NN) was much better than that of the backward-propagation-(BP)-based neural network (NN). This approach helped to realize the fast derivation of the secret key rate of CVQKD through an underwater channel, indicating that it can be used for improving performance in practical quantum communications.<\/jats:p>","DOI":"10.3390\/e25060937","type":"journal-article","created":{"date-parts":[[2023,6,15]],"date-time":"2023-06-15T02:28:56Z","timestamp":1686796136000},"page":"937","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Neural Network-Based Prediction for Secret Key Rate of Underwater Continuous-Variable Quantum Key Distribution through a Seawater Channel"],"prefix":"10.3390","volume":"25","author":[{"given":"Yun","family":"Mao","sequence":"first","affiliation":[{"name":"School of Information Engineering, Shaoyang University, Shaoyang 422000, China"},{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yiwu","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hui","family":"Hu","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gaofeng","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Shaoyang University, Shaoyang 422000, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jinguang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yijun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8147-9716","authenticated-orcid":false,"given":"Ying","family":"Guo","sequence":"additional","affiliation":[{"name":"School of Information Engineering, Shaoyang University, Shaoyang 422000, China"},{"name":"School of Computer Science, Beijing University of Posts and Telecommunications, Beijing 100876, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.tcs.2014.05.025","article-title":"Public key distribution and coin tossing","volume":"560","author":"Bennett","year":"2014","journal-title":"Theor. 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