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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "JATS-journalpublishing1-3.dtd">
<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 custom-type="elpub" pub-id-type="custom">najo-1524</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>Heterodyne Detection Method Of Multimode States for Subcarrier Wave Continuous Variable 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"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-4564-8284</contrib-id><name-alternatives><name name-style="western" xml:lang="en"><surname>Filipov</surname><given-names>Ilya Maksimovich</given-names></name></name-alternatives><email xlink:type="simple">imfilipov@itmo.ru</email><xref ref-type="aff" rid="aff-1"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-9081-8900</contrib-id><name-alternatives><name name-style="western" xml:lang="en"><surname>Goncharov</surname><given-names>Roman Konstantinovich</given-names></name></name-alternatives><email xlink:type="simple">rkgoncharov@itmo.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3919-4151</contrib-id><name-alternatives><name name-style="western" xml:lang="en"><surname>Dashkov</surname><given-names>Michael Victorovich</given-names></name></name-alternatives><email xlink:type="simple">m.dashkov@psuti.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><name-alternatives><name name-style="western" xml:lang="en"><surname>Bogdanova</surname><given-names>Ekaterina Igorevna</given-names></name></name-alternatives><email xlink:type="simple">ei.bogdanova@psuti.ru</email><xref ref-type="aff" rid="aff-3"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0003-0789-998X</contrib-id><name-alternatives><name name-style="western" xml:lang="en"><surname>Zinovev</surname><given-names>Alexandr Vyacheslavovich</given-names></name></name-alternatives><email xlink:type="simple">avzinovev@itmo.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-2414-3490</contrib-id><name-alternatives><name name-style="western" xml:lang="en"><surname>Chistiakov</surname><given-names>Vladimir Viktorovich</given-names></name></name-alternatives><email xlink:type="simple">v_chistyakov@itmo.ru</email><xref ref-type="aff" rid="aff-2"/></contrib><contrib contrib-type="author" corresp="yes"><contrib-id contrib-id-type="orcid">https://orcid.org/0000-0002-3894-511X</contrib-id><name-alternatives><name name-style="western" xml:lang="en"><surname>Kiselev</surname><given-names>Fedor Dmitrievich</given-names></name></name-alternatives><email xlink:type="simple">fdkiselev@itmo.ru</email><xref ref-type="aff" rid="aff-4"/></contrib></contrib-group><aff-alternatives id="aff-1"><aff xml:lang="ru"><institution>ITMO University</institution></aff><aff xml:lang="en"><institution>ITMO University, 199034, Saint Petersburg, Kadetskaya Line 3k2, Russia; SMARTS-Quanttelecom LLC, 199178, Saint Petersburg, Vasilievsky island 6 Line 59, Russia</institution></aff></aff-alternatives><aff xml:lang="en" id="aff-2"><institution>ITMO University, 199034, Saint Petersburg, Kadetskaya Line 3k2, Russia</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-3"><institution>Povolzhskiy State University of Telecommunications and Informatics (PSUTI), 443010, Samara, Moskovskoe Shosse St., 77, Russia</institution><country>Russian Federation</country></aff><aff xml:lang="en" id="aff-4"><institution>ITMO University, 199034, Saint Petersburg, Kadetskaya Line 3k2, Russia; SMARTS-Quanttelecom LLC, 199178, Saint Petersburg, Vasilievsky island 6 Line 59, Russia</institution><country>Russian Federation</country></aff><pub-date pub-type="collection"><year>2025</year></pub-date><pub-date pub-type="epub"><day>05</day><month>02</month><year>2026</year></pub-date><volume>16</volume><issue>6</issue><elocation-id>1524</elocation-id><permissions><copyright-statement>Copyright &amp;#x00A9; Filipov I.M., Goncharov R.K., Dashkov M.V., Bogdanova E.I., Zinovev A.V., Chistiakov V.V., Kiselev F.D., 2026</copyright-statement><copyright-year>2026</copyright-year><copyright-holder xml:lang="ru">Filipov I.M., Goncharov R.K., Dashkov M.V., Bogdanova E.I., Zinovev A.V., Chistiakov V.V., Kiselev F.D.</copyright-holder><copyright-holder xml:lang="en">Filipov I.M., Goncharov R.K., Dashkov M.V., Bogdanova E.I., Zinovev A.V., Chistiakov V.V., Kiselev F.D.</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/1524">https://nanojournal.ifmo.ru/jour/article/view/1524</self-uri><abstract><p>A novel coherent detection method for subcarrier wave (SCW) quantum states applied to continuous-variable quantum key distribution (CV-QKD) is presented. The proposed approach relies on repeated phase modulation at the receiver and spatial separation of the carrier and subcarrier frequency components. The resulting output is an intermediate frequency determined by the difference between the sender’s and receiver’s modulation frequencies. An analytical model of the detection output is developed, and a comparative analysis with alternative heterodyne detection methods is provided. Experimental validation confirms the linear dependence of the output signal on the receiver’s modulation frequency and the sender’s modulation index in the small-modulation regime. Furthermore, the feasibility of the proposed method is demonstrated through the detection of discretely modulated signals using quadrature phase-shift keying (QPSK).</p></abstract><kwd-group xml:lang="en"><kwd>coherent detection</kwd><kwd>subcarrier wave</kwd><kwd>continuous variable</kwd><kwd>quantum key distribution</kwd></kwd-group><funding-group><funding-statement xml:lang="en">the Russian Science Foundation (project No.24-11-00398)</funding-statement></funding-group></article-meta></front><back><ref-list><title>References</title></ref-list><fn-group><fn fn-type="conflict"><p>The authors declare that there are no conflicts of interest present.</p></fn></fn-group></back></article>
