{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:45:53Z","timestamp":1760060753093,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T00:00:00Z","timestamp":1758499200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ye Qixun Science Fund of the National Natural Science Foundation of China","award":["U2441219"],"award-info":[{"award-number":["U2441219"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A continuous-variable quantum key distribution (CVQKD) can be realized over the seawater channel, but the transmission of quantum signals in seawater media exhibits significant attenuation effects. Therefore, we propose an N-symbol amplitude and phase shift keying (N-APSK) modulation scheme to enhance the transmission performance of the CVQKD over the seawater channel. Specifically, an optimal N-APSK modulation scheme is designed based on the principle of maximizing the minimum Euclidean distance (MED). The simulation results show that the CVQKD protocol based on N-APSK modulation achieves a longer transmission distance over the seawater channel compared to the Gaussian modulation protocol. Additionally, increasing the value of N simultaneously expands the number of rings in the constellation diagram, further enhancing the communication distance. This study transfers modulation methods from the field of classical communications to the field of quantum communications, achieving a substantial improvement in communication distance and thereby promoting the integration of quantum communications and classical communications.<\/jats:p>","DOI":"10.3390\/e27090990","type":"journal-article","created":{"date-parts":[[2025,9,22]],"date-time":"2025-09-22T13:04:44Z","timestamp":1758546284000},"page":"990","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Continuous-Variable Quantum Key Distribution Based on N-APSK Modulation over Seawater Channel"],"prefix":"10.3390","volume":"27","author":[{"given":"Lei","family":"Mao","sequence":"first","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-8647-7575","authenticated-orcid":false,"given":"Zhangtao","family":"Liang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiyue","family":"Zuo","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hang","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yijun","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Automation, Central South University, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,9,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"057902","DOI":"10.1103\/PhysRevLett.88.057902","article-title":"Continuous Variable Quantum Cryptography Using Coherent States","volume":"88","author":"Grosshans","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"726","DOI":"10.1038\/nphys1018","article-title":"Continuous-variable quantum cryptography using two-way quantum communication","volume":"4","author":"Pirandola","year":"2008","journal-title":"Nat. Phys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"062337","DOI":"10.1103\/PhysRevA.92.062337","article-title":"Unidimensional continuous-variable quantum key distribution","volume":"92","author":"Usenko","year":"2015","journal-title":"Phys. Rev. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"010502","DOI":"10.1103\/PhysRevLett.125.010502","article-title":"Long-distance continuous-variable quantum keydistribution over 202.81 km of fiber","volume":"125","author":"Zhang","year":"2020","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"492","DOI":"10.1364\/OPTICA.450573","article-title":"Experimental demonstration of continuous-variable measurement-device-independent quantum key distribution over optical fiber","volume":"9","author":"Tian","year":"2022","journal-title":"Optica"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2953","DOI":"10.1364\/OL.492082","article-title":"High-performance long-distance discrete-modulation continuous-variable quantum key distribution","volume":"48","author":"Tian","year":"2023","journal-title":"Opt. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"10737","DOI":"10.1364\/OE.387402","article-title":"Phase compensation for free-space continuous-variablequantum key distribution","volume":"28","author":"Wang","year":"2020","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xu, S., Li, Y., Wang, Y., Mao, Y., Zuo, Z., Ruan, X., and Guo, Y. (2021). Noiseless attenuation for continuous-variable quantum key distribution over ground-satellite uplink. Appl. Sci., 11.","DOI":"10.3390\/app112311289"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1184","DOI":"10.1364\/OL.485166","article-title":"Experimental free-space continuous-variable quantum key distribution with thermal source","volume":"48","author":"Zhang","year":"2023","journal-title":"Opt. Lett."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"465302","DOI":"10.1088\/1751-8121\/abc220","article-title":"Atmospheric effects on satellite-mediated continuous-variable quantum key distribution","volume":"53","author":"Zuo","year":"2020","journal-title":"J. Phys. A Math. Theor."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"012417","DOI":"10.1103\/PhysRevA.103.012417","article-title":"Wavelength attack on atmospheric continuous-variable quantum key distribution","volume":"103","author":"Tan","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Mao, Y., Wu, X., Huang, W., Liao, Q., Deng, H., Wang, Y., and Guo, Y. (2020). Monte Carlo-based performance analysis for underwater continuous-variable quantum key distribution. Appl. Sci., 10.","DOI":"10.3390\/app10175744"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Feng, K., Wang, Y., Li, Y., Wang, Y., Zuo, Z., and Guo, Y. (2024). Underwater wavelength attack on discrete modulated continuous-variable quantum key distribution. Entropy, 26.","DOI":"10.3390\/e26060515"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2794","DOI":"10.1364\/OE.26.002794","article-title":"High key rate continuous-variable quantum key distribution with a real local oscillator","volume":"26","author":"Wang","year":"2018","journal-title":"Opt. Express"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"32882","DOI":"10.1364\/OE.404611","article-title":"High-speed Gaussian-modulated continuous-variable quantum key distribution with a local local oscillator based on pilot-tone-assisted phase compensation","volume":"28","author":"Wang","year":"2020","journal-title":"Opt. Express"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ren, S., Yang, S., Wonfor, A., White, I., and Penty, R. (2021). Demonstration of high-speed and low-complexity continuous variable quantum key distribution system with local local oscillator. Sci. Rep., 11.","DOI":"10.1038\/s41598-021-88468-1"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1588","DOI":"10.1364\/OL.42.001588","article-title":"Continuous variable quantum key distribution with a real local oscillator using simultaneous pilot signals","volume":"42","author":"Kleis","year":"2017","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1038\/s42005-022-00941-z","article-title":"Sub-Gbps key rate four-state continuous-variable quantum key distribution within metropolitan area","volume":"5","author":"Wang","year":"2022","journal-title":"Commun. Phys."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"040306","DOI":"10.1103\/PRXQuantum.4.040306","article-title":"Finite-size security for discrete-modulated continuous-variable quantum key distribution protocols","volume":"4","author":"Kanitschar","year":"2023","journal-title":"PRX Quantum"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"38669","DOI":"10.1364\/OE.439992","article-title":"Secret key rate of multi-ring M-APSK continuous variable quantum key distribution","volume":"29","author":"Almeida","year":"2021","journal-title":"Opt. Express"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"3948","DOI":"10.1364\/OL.456333","article-title":"Probabilistic shaped 128-APSK CV-QKD transmission system over optical fibres","volume":"47","author":"Pereira","year":"2022","journal-title":"Opt. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1140\/epjqt\/s40507-023-00176-z","article-title":"Impact of transmitter imbalances on the security of continuous variables quantum key distribution","volume":"10","author":"Pereira","year":"2023","journal-title":"EPJ Quantum Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"6134","DOI":"10.1109\/JLT.2023.3280076","article-title":"Reconciliation efficiency impact on discrete modulated CV-QKD systems key rates","volume":"41","author":"Almeida","year":"2023","journal-title":"J. Light. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"261","DOI":"10.1002\/sat.841","article-title":"Turbo-coded APSK modulations design for satellite broadband communications","volume":"24","author":"Martinez","year":"2006","journal-title":"Int. J. Satell. Commun. Netw."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1109\/LCOMM.2011.101211.111825","article-title":"APSK constellation with Gray mapping","volume":"15","author":"Liu","year":"2011","journal-title":"IEEE Commun. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"21509","DOI":"10.1364\/OE.25.021509","article-title":"Security weaknesses of underwater wireless optical communication","volume":"25","author":"Kong","year":"2017","journal-title":"Opt. Express"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"15702","DOI":"10.1364\/OE.15.015702","article-title":"Fluorescence component in the reflectance spectra from coastal waters. Dependence on water composition","volume":"15","author":"Gilerson","year":"2007","journal-title":"Opt. Express"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"671","DOI":"10.4319\/lo.1981.26.4.0671","article-title":"An optical classification of coastal and oceanic waters based on the specific spectral absorption curves of phytoplankton pigments, dissolved organic matter, and other particulate materials 1","volume":"26","author":"Prieur","year":"1981","journal-title":"Limnol. Oceanogr."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"C8","DOI":"10.1029\/2005JC003207","article-title":"Vertical distribution of phytoplankton communities in open ocean: An assessment based on surface chlorophyll","volume":"111","author":"Uitz","year":"2006","journal-title":"J. Geophys. Res. Ocean."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/9\/990\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:47:01Z","timestamp":1760035621000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/27\/9\/990"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9,22]]},"references-count":29,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2025,9]]}},"alternative-id":["e27090990"],"URL":"https:\/\/doi.org\/10.3390\/e27090990","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2025,9,22]]}}}