najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2025-16-6-778-784najo-1617Research ArticlePHYSICSФИЗИКАHeterodyne detection method of multimode states for subcarrier wave continuous variable quantum key distributionМетод гетеродинного детектирования многомодовых состояний для квантового распределения ключа на непрерывных переменных с использованием боковых частотhttps://orcid.org/0000-0003-4564-8284ФилиповИ. М.FilipovI. M.

Ilya Filipov

Saint Petersburg, Kadetskaya Line 3k2; 199178, Saint Petersburg, Vasilievsky island 6 Line 59

imfilipov@itmo.ruhttps://orcid.org/0000-0002-9081-8900ГончаровР. К.GoncharovR. K.

Roman Goncharov

199034, Saint Petersburg, Kadetskaya Line 3k2

rkgoncharov@itmo.ruhttps://orcid.org/0000-0002-3919-4151ДашковМ. В.DashkovM. V.

Michael Dashkov

443010, Samara, Moskovskoe Shosse St., 77

m.dashkov@psuti.ruБогдановаЕ. И.BogdanovaE. I.

Ekaterina Bogdanova

443010, Samara, Moskovskoe Shosse St., 77

ei.bogdanova@psuti.ruhttps://orcid.org/0000-0003-0789-998XЗиновьевА. В.ZinovevA. V.

Alexandr Zinovev

199034, Saint Petersburg, Kadetskaya Line 3k2

avzinovev@itmo.ruhttps://orcid.org/0000-0002-2414-3490ЧистяковВ. В.ChistiakovV. V.

Vladimir Chistiakov

199034, Saint Petersburg, Kadetskaya Line 3k2

v_chistyakov@itmo.ruhttps://orcid.org/0000-0002-3894-511XКиселевФ. Д.KiselevF. D.

 Fedor Kiselev

199034, Saint Petersburg, Kadetskaya Line 3k2; 199178, Saint Petersburg, Vasilievsky island 6 Line 59

fdkiselev@itmo.ruITMO University; SMARTS-Quanttelecom LLCRussian FederationITMO UniversityRussian FederationPovolzhskiy State University of Telecommunications and Informatics (PSUTI)Russian Federation202506012026166778784Copyright © Filipov I.M., Goncharov R.K., Dashkov M.V., Bogdanova E.I., Zinovev A.V., Chistiakov V.V., Kiselev F.D., 20262026Филипов И.М., Гончаров Р.К., Дашков М.В., Богданова Е.И., Зиновьев А.В., Чистяков В.В., Киселев Ф.Д.Filipov I.M., Goncharov R.K., Dashkov M.V., Bogdanova E.I., Zinovev A.V., Chistiakov V.V., Kiselev F.D.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1617

A novel coherent detection method for subcarrier wave (SCW) quantum states applied to continuousvariable 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 through time-varying modulation using a classical method based on Bessel functions, 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).

Представлен новый метод когерентного детектирования квантовых состояний на боковых частотах (БЧ), применяемый в квантовом распределении ключа на непрерывных переменных (КРК-НП). Предлагаемый подход основан на повторной фазовой модуляции на стороне приемника и пространственном разделении частотных компонент несущей и боковых частот. Выходным сигналом является промежуточная частота, определяемая разностью между частотами модуляции отправителя и получателя. Разработана аналитическая модель выходного сигнала детектора с использованием зависящей от времени модуляции на основе классического метода с функциями Бесселя, и проведен сравнительный анализ с альтернативными методами гетеродинного детектирования. Экспериментальная проверка подтверждает линейную зависимость выходного сигнала от частоты модуляции приемника и индекса модуляции отправителя в режиме малого индекса модуляции. Кроме того, продемонстрирована осуществимость предложенного метода путем детектирования дискретно модулированных сигналов с использованием квадратурной фазовой манипуляции (QPSK).

 

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The authors declare that there are no conflicts of interest present.