{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,4]],"date-time":"2026-06-04T15:15:44Z","timestamp":1780586144421,"version":"3.54.1"},"reference-count":65,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T00:00:00Z","timestamp":1696896000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004715","name":"Defence Science and Technology Group, Next Generation Technology Fund","doi-asserted-by":"publisher","award":["MyIP 8672"],"award-info":[{"award-number":["MyIP 8672"]}],"id":[{"id":"10.13039\/501100004715","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>Continuous-variable quantum key distribution (CV-QKD) shows potential for the rapid development of an information-theoretic secure global communication network; however, the complexities of CV-QKD implementation remain a restrictive factor. Machine learning (ML) has recently shown promise in alleviating these complexities. ML has been applied to almost every stage of CV-QKD protocols, including ML-assisted phase error estimation, excess noise estimation, state discrimination, parameter estimation and optimization, key sifting, information reconciliation, and key rate estimation. This survey provides a comprehensive analysis of the current literature on ML-assisted CV-QKD. In addition, the survey compares the ML algorithms assisting CV-QKD with the traditional algorithms they aim to augment, as well as providing recommendations for future directions for ML-assisted CV-QKD research.<\/jats:p>","DOI":"10.3390\/info14100553","type":"journal-article","created":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T06:14:04Z","timestamp":1696918444000},"page":"553","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A Survey of Machine Learning Assisted Continuous-Variable Quantum Key Distribution"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9969-082X","authenticated-orcid":false,"given":"Nathan K.","family":"Long","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Telecommunications, University of New South Wales, Kensington, NSW 2010, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9672-5601","authenticated-orcid":false,"given":"Robert","family":"Malaney","sequence":"additional","affiliation":[{"name":"School of Electrical Engineering and Telecommunications, University of New South Wales, Kensington, NSW 2010, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenneth J.","family":"Grant","sequence":"additional","affiliation":[{"name":"Sensors and Effectors Division, Defence Science and Technology Group, Edinburgh, SA 5111, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1038\/s41534-023-00695-8","article-title":"Continuous-mode quantum key distribution with digital signal processing","volume":"9","author":"Chen","year":"2023","journal-title":"NPJ Quantum Inf."},{"key":"ref_2","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_3","doi-asserted-by":"crossref","first-page":"032309","DOI":"10.1103\/PhysRevA.86.032309","article-title":"Analysis of imperfections in practical continuous-variable quantum key distribution","volume":"86","author":"Jouguet","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"022315","DOI":"10.1103\/PhysRevA.95.022315","article-title":"Phase-noise limitations in continuous-variable quantum key distribution with homodyne detection","volume":"95","author":"Corvaja","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1038\/s41534-021-00361-x","article-title":"Machine learning aided carrier recovery in continuous-variable quantum key distribution","volume":"7","author":"Chin","year":"2021","journal-title":"NPJ Quantum Inf."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Chin, H.M., Hajomer, A.A., Jain, N., Andersen, U.L., and Gehring, T. (2023, January 24\u201328). Machine learning based joint polarization and phase compensation for CV-QKD. Proceedings of the Optical Fiber Communication Conference (OFC), San Diego, CA, USA.","DOI":"10.1364\/OFC.2023.Th3J.2"},{"key":"ref_7","unstructured":"Hajomer, A.A., Mani, H., Jain, N., Chin, H.M., Andersen, U.L., and Gehring, T. (2022, January 18\u201322). Continuous-Variable Quantum Key Distribution Over 60 km Optical Fiber with Real Local Oscillator. Proceedings of the European Conference on Optical Communication (ECOC), Basel, Switzerland."},{"key":"ref_8","unstructured":"Hajomer, A.A., Derkach, I., Jain, N., Chin, H.M., Andersen, U.L., and Gehring, T. (2023). Long-distance continuous-variable quantum key distribution over 100 km fiber with local local oscillator. arXiv."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"136","DOI":"10.1038\/s41534-022-00640-1","article-title":"Modulation leakage-free continuous-variable quantum key distribution","volume":"8","author":"Hajomer","year":"2022","journal-title":"NPJ Quantum Inf."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"4740","DOI":"10.1038\/s41467-022-32161-y","article-title":"Practical continuous-variable quantum key distribution with composable security","volume":"13","author":"Jain","year":"2022","journal-title":"Nat. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Jain, N., Derkach, I., Chin, H.M., Filip, R., Andersen, U.L., Usenko, V.C., and Gehring, T. (2022, January 7\u20138). Modulator vulnerability in continuous-variable quantum key distribution. Proceedings of the Emerging Imaging and Sensing Technologies for Security and Defence VII, International Society for Optics and Photonics, SPIE, Birmingham UK.","DOI":"10.1117\/12.2638795"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Liang, K., Chai, G., Cao, Z., Wang, Q., Wang, L., and Peng, J. (2022). Machine Learning assisted excess noise suppression for continuous-variable quantum key distribution. arXiv.","DOI":"10.1103\/PhysRevApplied.18.054077"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Xing, Z., Li, X., Ruan, X., Luo, Y., and Zhang, H. (2022). Phase Compensation for Continuous Variable Quantum Key Distribution Based on Convolutional Neural Network. Photonics, 9.","DOI":"10.3390\/photonics9070463"},{"key":"ref_14","first-page":"1","article-title":"Neural Network-Powered Nonlinear Compensation Framework for High-Speed Continuous Variable Quantum Key Distribution","volume":"14","author":"Zhang","year":"2022","journal-title":"IEEE Photonics J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"062614","DOI":"10.1103\/PhysRevA.107.062614","article-title":"Automatic phase compensation of a continuous-variable quantum-key-distribution system via deep learning","volume":"107","author":"Zhang","year":"2023","journal-title":"Phys. Rev. A"},{"key":"ref_16","unstructured":"Long, N.K., Malaney, R., and Grant, K.J. (2023). Phase Correction using Deep Learning for Satellite-to-Ground CV-QKD. arXiv."},{"key":"ref_17","unstructured":"Kleis, S., Rueckmann, M., and Schaeffer, C.G. (2019). Continuous-variable quantum key distribution with a real local oscillator and without auxiliary signals. arXiv."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"R\u00fcckmann, M., Kleis, S., Schaeffer, C.G., and Zibar, D. (2020, January 13\u201316). Machine Learning in Quantum Communication. Proceedings of the OSA Advanced Photonics Congress (AP) 2020 (IPR, NP, NOMA, Networks, PVLED, PSC, SPPCom, SOF), Washington, DC, USA.","DOI":"10.1364\/SPPCOM.2020.SpTu3I.6"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"R\u00fcckmann, M., Kleis, S., and Schaeffer, C.G. (2020, January 8\u201312). 17 GBd Sub-Photon Level Heterodyne Detection for CV-QKD Enabled by Machine Learning. Proceedings of the Optical Fiber Communication Conference (OFC), San Diego, CA, USA.","DOI":"10.1364\/OFC.2020.Th2A.54"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11128-018-1877-y","article-title":"Recurrent neural network approach to quantum signal: Coherent state restoration for continuous-variable quantum key distribution","volume":"17","author":"Lu","year":"2018","journal-title":"Quantum Inf. Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"066109","DOI":"10.1117\/1.OE.57.6.066109","article-title":"Discrete-modulated continuous-variable quantum key distribution with a machine-learning-based detector","volume":"57","author":"Li","year":"2018","journal-title":"Opt. Eng."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"083086","DOI":"10.1088\/1367-2630\/abab3c","article-title":"Multi-label learning for improving discretely-modulated continuous-variable quantum key distribution","volume":"22","author":"Liao","year":"2020","journal-title":"New J. Phys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"B51","DOI":"10.1364\/JOSAB.36.000B51","article-title":"Blind modulation format identification using the DBSCAN algorithm for continuous-variable quantum key distribution","volume":"36","author":"Zhang","year":"2019","journal-title":"JOSA B"},{"key":"ref_24","unstructured":"Liao, Q., Liu, J., Huang, A., Huang, L., Fei, Z., and Fu, X. (2023). High-rate discretely-modulated CV-QKD using quantum machine learning. arXiv."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"022316","DOI":"10.1103\/PhysRevA.97.022316","article-title":"Integrating machine learning to achieve an automatic parameter prediction for practical continuous-variable quantum key distribution","volume":"97","author":"Liu","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Su, Y., Guo, Y., and Huang, D. (2019). Parameter Optimization Based BPNN of Atmosphere Continuous-Variable Quantum Key Distribution. Entropy, 21.","DOI":"10.3390\/e21090908"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"042411","DOI":"10.1103\/PhysRevA.105.042411","article-title":"Beyond universal attack detection for continuous-variable quantum key distribution via deep learning","volume":"105","author":"Luo","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"012616","DOI":"10.1103\/PhysRevA.104.012616","article-title":"Key-sifting algorithms for continuous-variable quantum key distribution","volume":"104","author":"Jin","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Xie, J., Zhang, L., Wang, Y., and Huang, D. (2022). Deep Neural Network Based Reconciliation for CV-QKD. Photonics, 9.","DOI":"10.3390\/photonics9020110"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"8879","DOI":"10.1038\/s41598-022-12647-x","article-title":"Neural network-based prediction of the secret-key rate of quantum key distribution","volume":"12","author":"Zhou","year":"2022","journal-title":"Sci. Rep."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"15024","DOI":"10.1364\/OE.455762","article-title":"Automated machine learning for secure key rate in discrete-modulated continuous-variable quantum key distribution","volume":"30","author":"Liu","year":"2022","journal-title":"Opt. Express"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"012316","DOI":"10.1103\/PhysRevA.100.012316","article-title":"Quantum hacking of free-space continuous-variable quantum key distribution by using a machine-learning technique","volume":"100","author":"Huang","year":"2019","journal-title":"Phys. Rev. A"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zheng, Y., Shi, H., Pan, W., Wang, Q., and Mao, J. (2021). Quantum Hacking on an Integrated Continuous-Variable Quantum Key Distribution System via Power Analysis. Entropy, 23.","DOI":"10.3390\/e23020176"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"083073","DOI":"10.1088\/1367-2630\/aba8d4","article-title":"Detecting quantum attacks: A machine learning based defense strategy for practical continuous-variable quantum key distribution","volume":"22","author":"Mao","year":"2020","journal-title":"New J. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"062320","DOI":"10.1103\/PhysRevA.101.062320","article-title":"Hidden-Markov-model-based calibration-attack recognition for continuous-variable quantum key distribution","volume":"101","author":"Mao","year":"2020","journal-title":"Phys. Rev. A"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1364\/JOSAB.386394","article-title":"Wavelength attack recognition based on machine learning optical spectrum analysis for the practical continuous-variable quantum key distribution system","volume":"37","author":"He","year":"2020","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Al-Mohammed, H.A., Al-Ali, A., Yaacoub, E., Abualsaud, K., and Khattab, T. (2021, January 7\u201311). Detecting Attackers during Quantum Key Distribution in IoT Networks using Neural Networks. Proceedings of the 2021 IEEE Globecom Workshops, Madrid, Spain.","DOI":"10.1109\/GCWkshps52748.2021.9681988"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"022607","DOI":"10.1103\/PhysRevA.106.022607","article-title":"Detecting practical quantum attacks for continuous-variable quantum key distribution using density-based spatial clustering of applications with noise","volume":"106","author":"Liao","year":"2022","journal-title":"Phys. Rev. A"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1364\/JOSAB.441802","article-title":"Sifting scheme for continuous-variable quantum key distribution with short samples","volume":"39","author":"Wu","year":"2022","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"127694","DOI":"10.1016\/j.physleta.2021.127694","article-title":"Ensemble learning for failure prediction of underwater continuous variable quantum key distribution with discrete modulations","volume":"419","author":"Li","year":"2021","journal-title":"Phys. Lett. A"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Guo, Y., Yin, P., and Huang, D. (2023). One-Pixel Attack for Continuous-Variable Quantum Key Distribution Systems. Photonics, 10.","DOI":"10.3390\/photonics10020129"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Li, S., Yin, P., Zhou, Z., Tang, J., Huang, D., and Zhang, L. (2023). Dictionary Learning Based Scheme for Adversarial Defense in Continuous-Variable Quantum Key Distribution. Entropy, 25.","DOI":"10.3390\/e25030499"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Huang, D., Liu, S., and Zhang, L. (2021). Secure Continuous-Variable Quantum Key Distribution with Machine Learning. Photonics, 12.","DOI":"10.3390\/photonics8110511"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"010301","DOI":"10.1103\/PRXQuantum.1.010301","article-title":"Machine learning for long-distance quantum communication","volume":"1","author":"Melnikov","year":"2020","journal-title":"PRX Quantum"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TQE.2021.3137559","article-title":"Machine-learning-based parameter estimation of gaussian quantum states","volume":"3","author":"Kundu","year":"2021","journal-title":"IEEE Trans. Quantum Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"12410","DOI":"10.1038\/s41598-019-48551-0","article-title":"Continuous-variable quantum phase estimation based on machine learning","volume":"9","author":"Xiao","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_47","first-page":"1","article-title":"Machine Learning Assisted Prediction for Free-Space Continuous Variable Quantum Teleportation","volume":"14","author":"Xu","year":"2022","journal-title":"IEEE Photonics J."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Gerry, C., and Knight, P.L. (2005). Introductory Quantum Optics, Cambridge University Press.","DOI":"10.1017\/CBO9780511791239"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1800011","DOI":"10.1002\/qute.201800011","article-title":"Continuous-Variable Quantum Key Distribution with Gaussian Modulation\u2014The Theory of Practical Implementations","volume":"1","author":"Laudenbach","year":"2018","journal-title":"Adv. Quantum Technol."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"6072","DOI":"10.3390\/e17096072","article-title":"Distributing secret keys with quantum continuous variables: Principle, security and implementations","volume":"17","author":"Diamanti","year":"2015","journal-title":"Entropy"},{"key":"ref_51","first-page":"041064","article-title":"Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution","volume":"9","author":"Lin","year":"2019","journal-title":"Phys. Rev. X"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"180504","DOI":"10.1103\/PhysRevLett.102.180504","article-title":"Unconditional security proof of long-distance continuous-variable quantum key distribution with discrete modulation","volume":"102","author":"Leverrier","year":"2009","journal-title":"Phys. Rev. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"042312","DOI":"10.1103\/PhysRevA.83.042312","article-title":"Continuous-variable quantum-key-distribution protocols with a non-Gaussian modulation","volume":"83","author":"Leverrier","year":"2011","journal-title":"Phys. Rev. A"},{"key":"ref_54","first-page":"1","article-title":"Optimized-eight-state CV-QKD protocol outperforming Gaussian modulation based protocols","volume":"11","author":"Djordjevic","year":"2019","journal-title":"IEEE Photonics J."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"020306","DOI":"10.1088\/1674-1056\/ac2807","article-title":"Parameter estimation of continuous variable quantum key distribution system via artificial neural networks","volume":"31","author":"Luo","year":"2022","journal-title":"Chin. Phys. B"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"062313","DOI":"10.1103\/PhysRevA.87.062313","article-title":"Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution","volume":"87","author":"Jouguet","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"012310","DOI":"10.1103\/PhysRevA.97.012310","article-title":"Pilot-multiplexed continuous-variable quantum key distribution with a real local oscillator","volume":"97","author":"Wang","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Kish, S.P., Villase\u00f1or, E., Malaney, R., Mudge, K.A., and Grant, K.J. (2021, January 14\u201323). Use of a local local oscillator for the satellite-to-earth channel. Proceedings of the IEEE International Conference on Communications, Montreal, QC, Canada.","DOI":"10.1109\/ICC42927.2021.9500392"},{"key":"ref_59","unstructured":"Garcia-Callejo, A., Ruiz-Chamorro, A., Cano, D., and Fernandez, V. (December, January 29). A Review on Continuous-Variable Quantum Key Distribution Security. Proceedings of the International Conference on Ubiquitous Computing and Ambient Intelligence, C\u00f3rdoba, Spain."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"012316","DOI":"10.1103\/PhysRevA.95.012316","article-title":"Self-coherent phase reference sharing for continuous-variable quantum key distribution","volume":"95","author":"Marie","year":"2017","journal-title":"Phys. Rev. A"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"032608","DOI":"10.1103\/PhysRevA.104.032608","article-title":"Phase noise model for continuous-variable quantum key distribution using a local local oscillator","volume":"104","author":"Shao","year":"2021","journal-title":"Phys. Rev. A"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Villase\u00f1or, E., Malaney, R., Mudge, K.A., and Grant, K.J. (2020, January 7\u201311). Atmospheric effects on satellite-to-ground quantum key distribution using coherent states. Proceedings of the IEEE Global Communications Conference, Taipei, Taiwan.","DOI":"10.1109\/GLOBECOM42002.2020.9348086"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1007\/s42979-021-00592-x","article-title":"Machine learning: Algorithms, real-world applications and research directions","volume":"2","author":"Sarker","year":"2021","journal-title":"SN Comput. Sci."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"023015","DOI":"10.1088\/1367-2630\/aaa8c4","article-title":"Long-distance continuous-variable quantum key distribution using non-Gaussian state-discrimination detection","volume":"20","author":"Liao","year":"2018","journal-title":"New J. Phys."},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Okey, O.D., Maidin, S.S., Lopes Rosa, R., Toor, W.T., Carrillo Melgarejo, D., Wuttisittikulkij, L., Saadi, M., and Zegarra Rodr\u00edguez, D. (2022). Quantum key distribution protocol selector based on machine learning for next-generation networks. Sustainability, 14.","DOI":"10.3390\/su142315901"}],"container-title":["Information"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2078-2489\/14\/10\/553\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:04:11Z","timestamp":1760130251000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2078-2489\/14\/10\/553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,10]]},"references-count":65,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2023,10]]}},"alternative-id":["info14100553"],"URL":"https:\/\/doi.org\/10.3390\/info14100553","relation":{},"ISSN":["2078-2489"],"issn-type":[{"value":"2078-2489","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,10]]}}}