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<article article-type="research-article" dtd-version="1.3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xml:lang="en"><front><journal-meta><journal-id journal-id-type="publisher-id">najo</journal-id><journal-title-group><journal-title xml:lang="en">Nanosystems: Physics, Chemistry, Mathematics</journal-title><trans-title-group xml:lang="ru"><trans-title>Наносистемы: физика, химия, математика</trans-title></trans-title-group></journal-title-group><issn pub-type="ppub">2220-8054</issn><issn pub-type="epub">2305-7971</issn><publisher><publisher-name>Университет ИТМО</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.17586/2220-8054-2020-11-6-651-658</article-id><article-id custom-type="elpub" pub-id-type="custom">najo-363</article-id><article-categories><subj-group subj-group-type="heading"><subject>Research Article</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="en"><subject>PHYSICS</subject></subj-group><subj-group subj-group-type="section-heading" xml:lang="ru"><subject>ФИЗИКА</subject></subj-group></article-categories><title-group><article-title>On quantum bit coding by Gaussian beam modes for the quantum key distribution</article-title><trans-title-group xml:lang="ru"><trans-title></trans-title></trans-title-group></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Faleeva</surname><given-names>M. P.</given-names></name></name-alternatives><bio xml:lang="en"><p>Kronverkskiy, 49, Saint Petersburg, 197101</p></bio><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Popov</surname><given-names>I. Y.</given-names></name></name-alternatives><bio xml:lang="en"><p>Kronverkskiy, 49, Saint Petersburg, 197101</p></bio><email xlink:type="simple">popov1955@gmail.com</email><xref ref-type="aff" rid="aff-1"/></contrib></contrib-group><aff xml:lang="en" id="aff-1"><institution>ITMO University</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2020</year></pub-date><pub-date pub-type="epub"><day>29</day><month>07</month><year>2025</year></pub-date><volume>11</volume><issue>6</issue><elocation-id>651–658</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Faleeva M.P., Popov I.Y., 2025</copyright-statement><copyright-year>2025</copyright-year><copyright-holder xml:lang="ru">Faleeva M.P., Popov I.Y.</copyright-holder><copyright-holder xml:lang="en">Faleeva M.P., Popov I.Y.</copyright-holder><license xml:lang="ru" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>Данная работа распространяется под лицензией Creative Commons Attribution 4.0.</license-p></license><license xml:lang="en" license-type="creative-commons-attribution" xlink:href="https://creativecommons.org/licenses/by/4.0/" xlink:type="simple"><license-p>This work is licensed under a Creative Commons Attribution 4.0 License.</license-p></license></permissions><self-uri xlink:href="https://nanojournal.ifmo.ru/jour/article/view/363">https://nanojournal.ifmo.ru/jour/article/view/363</self-uri><abstract><p>This paper deals with possibility of implementation of quantum key distribution algorithm through turbulent atmosphere. Beam wandering is considered as the main perturbation. For description of the density matrix, the Glauber–Sudarshan P-function technique is used. The probabilities of detectors triggering are determined.</p></abstract><kwd-group xml:lang="en"><kwd>quantum bit</kwd><kwd>gaussian beam</kwd><kwd>entanglement</kwd><kwd>quantum key distribution</kwd></kwd-group><funding-group><funding-statement xml:lang="en">The reported study was funded by RFBR, project number 19-31-90154.</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title><ref id="cit1"><label>1</label><citation-alternatives><mixed-citation xml:lang="ru">Derkach I., Usenko V.C., Filip R. Squeezing-enhanced quantum key distribution over atmospheric channels. New J. Phys., 2020, 22, P. 053006.</mixed-citation><mixed-citation xml:lang="en">Derkach I., Usenko V.C., Filip R. Squeezing-enhanced quantum key distribution over atmospheric channels. New J. 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