{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T09:47:43Z","timestamp":1776764863285,"version":"3.51.2"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,24]],"date-time":"2021-09-24T00:00:00Z","timestamp":1632441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["Nos. 12074194, 11774180"],"award-info":[{"award-number":["Nos. 12074194, 11774180"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["Nos. 2017YFA0304100, 2018YFA0306400"],"award-info":[{"award-number":["Nos. 2017YFA0304100, 2018YFA0306400"]}]},{"name":"Leading-edge technology Program of Jiangsu Natural Science Foundation","award":["No. BK20192001"],"award-info":[{"award-number":["No. BK20192001"]}]},{"name":"NUPTSF","award":["No. NY220122, NY220123"],"award-info":[{"award-number":["No. NY220122, NY220123"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In most of the realistic measurement device-independent quantum key distribution (MDI-QKD) systems, efficient, real-time feedback controls are required to maintain system stability when facing disturbance from either external environment or imperfect internal components. Traditionally, people either use a \u201cscanning-and-transmitting\u201d program or insert an extra device to make a phase reference frame calibration for a stable high-visibility interference, resulting in higher system complexity and lower transmission efficiency. In this work, we build a machine learning-assisted MDI-QKD system, where a machine learning model\u2014the long short-term memory (LSTM) network\u2014is for the first time to apply onto the MDI-QKD system for reference frame calibrations. In this machine learning-assisted MDI-QKD system, one can predict out the phase drift between the two users in advance, and actively perform real-time phase compensations, dramatically increasing the key transmission efficiency. Furthermore, we carry out corresponding experimental demonstration over 100 km and 250 km commercial standard single-mode fibers, verifying the effectiveness of the approach.<\/jats:p>","DOI":"10.3390\/e23101242","type":"journal-article","created":{"date-parts":[[2021,9,24]],"date-time":"2021-09-24T20:15:32Z","timestamp":1632514532000},"page":"1242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Machine Learning-Assisted Measurement Device-Independent Quantum Key Distribution on Reference Frame Calibration"],"prefix":"10.3390","volume":"23","author":[{"given":"Sihao","family":"Zhang","sequence":"first","affiliation":[{"name":"Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Broadband Wireless Communication and Sensor Network Technology, Key Lab of Ministry of Education, Nanjing 210003, China"},{"name":"Telecommunication and Networks, National Engineering Research Center, NUPT, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6661-2358","authenticated-orcid":false,"given":"Jingyang","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Broadband Wireless Communication and Sensor Network Technology, Key Lab of Ministry of Education, Nanjing 210003, China"},{"name":"Telecommunication and Networks, National Engineering Research Center, NUPT, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guigen","family":"Zeng","sequence":"additional","affiliation":[{"name":"Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Broadband Wireless Communication and Sensor Network Technology, Key Lab of Ministry of Education, Nanjing 210003, China"},{"name":"Telecommunication and Networks, National Engineering Research Center, NUPT, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunhui","family":"Zhang","sequence":"additional","affiliation":[{"name":"Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Broadband Wireless Communication and Sensor Network Technology, Key Lab of Ministry of Education, Nanjing 210003, China"},{"name":"Telecommunication and Networks, National Engineering Research Center, NUPT, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xingyu","family":"Zhou","sequence":"additional","affiliation":[{"name":"Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Broadband Wireless Communication and Sensor Network Technology, Key Lab of Ministry of Education, Nanjing 210003, China"},{"name":"Telecommunication and Networks, National Engineering Research Center, NUPT, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6314-4250","authenticated-orcid":false,"given":"Qin","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Quantum Information and Technology, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"},{"name":"Broadband Wireless Communication and Sensor Network Technology, Key Lab of Ministry of Education, Nanjing 210003, China"},{"name":"Telecommunication and Networks, National Engineering Research Center, NUPT, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1103\/PhysRevLett.85.441","article-title":"Simple proof of security of the BB84 quantum key distribution protocol","volume":"85","author":"Shor","year":"2000","journal-title":"Phys. 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