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Heterodyne detection method of multimode states for subcarrier wave continuous variable quantum key distribution

https://doi.org/10.17586/2220-8054-2025-16-6-778-784

Abstract

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).

About the Authors

I. M. Filipov
ITMO University; SMARTS-Quanttelecom LLC
Russian Federation

Ilya Filipov

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



R. K. Goncharov
ITMO University
Russian Federation

Roman Goncharov

199034, Saint Petersburg, Kadetskaya Line 3k2



M. V. Dashkov
Povolzhskiy State University of Telecommunications and Informatics (PSUTI)
Russian Federation

Michael Dashkov

443010, Samara, Moskovskoe Shosse St., 77



E. I. Bogdanova
Povolzhskiy State University of Telecommunications and Informatics (PSUTI)
Russian Federation

Ekaterina Bogdanova

443010, Samara, Moskovskoe Shosse St., 77



A. V. Zinovev
ITMO University
Russian Federation

Alexandr Zinovev

199034, Saint Petersburg, Kadetskaya Line 3k2



V. V. Chistiakov
ITMO University
Russian Federation

Vladimir Chistiakov

199034, Saint Petersburg, Kadetskaya Line 3k2



F. D. Kiselev
ITMO University; SMARTS-Quanttelecom LLC
Russian Federation

 Fedor Kiselev

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



References

1. Pirandola S., Andersen U. L., Banchi L., Berta M., Bunandar D., Colbeck R., Englund D., Gehring T., Lupo C., Ottaviani C., Pereira J.L., Razavi M., Shamsul Shaari J., Tomamichel M., Usenko V.C., Vallone G., Villoresi P., and Wallden P. Advances in quantum cryptography. Advances in optics and photonics, 2020, 12(4), P. 1012–1236.

2. Zhang G., Haw J.Y., Cai H., Xu F., Assad S., Fitzsimons J.F., Zhou X., Zhang Y., Yu S., Wu J., Ser W. An integrated silicon photonic chip platform for continuous-variable quantum key distribution. Nature Photonics, 2019, 13(12), P. 839–842.

3. Hajomer A.A. , Bruynsteen C., Derkach I., Jain N., Bomhals A., Bastiaens S., Andersen U.L., Yin X., and Gehring T. Continuous-variable quantum key distribution at 10 gbaud using an integrated photonic-electronic receiver. Optica, 2024, 11(9), P. 1197–1204.

4. Pietri Y.,Trigo Vidarte L., Schiavon M., Vivien L., Grangier P., Rhouni A., and Diamanti E. Experimental demonstration of continuous-variable ´ quantum key distribution with a silicon photonics integrated receiver. Optica Quantum, 2024, 2(6), P. 428–437.

5. Hajomer A.A., Derkach I., Usenko V.C., Andersen U.L., and Gehring T. Coexistence of continuous-variable quantum key distribution and classical data over 120-km fiber. arXiv preprint arXiv:2502.17388, 2025.

6. Milovancev D., Voki ˇ c N., Laudenbach F., Pacher C., H ´ ubel H., and Schrenk B. High rate cv-qkd secured mobile wdm fronthaul for dense 5 g radio ¨ networks. Journal of Lightwave Technology, 2021, 39(11), P. 3445–3457.

7. Zhang Y., Bian Y., Li Z., Yu S., and Guo H. Continuous-variable quantum key distribution system: Past, present, and future. Applied Physics Reviews, 2024, 11(1).

8. Samsonov E., Goncharov R., Gaidash A., Kozubov A., Egorov V., and Gleim A. Subcarrier wave continuous variable quantum key distribution with discrete modulation: mathematical model and finite-key analysis. Scientific Reports, 2020, 10(1), P. 10034.

9. Su Z., Wang J., Cai D., Guo X., Wang D., and Li Z. Experimental demonstration of phase sensitive multimode continuous variable quantum key distribution with improved secure key rate. Photonics Research, 2023, 11(11).

10. Samsonov E., Goncharov R., Fadeev M., Zinoviev A., Kirichenko D., Nasedkin B., Kiselev A., and Egorov V. Coherent detection schemes for subcarrier wave continuous variable quantum key distribution. Journal of the Optical Society of America B: Optical Physics, 2021, 38(7), P. 2215– 2222.

11. Goncharov R., Kiselev A., Samsonov E., and Egorov V. Subcarrier wave continuous-variable quantum key distribution with gaussian modulation: composable security analysis. Computer Optics, 2023, 47(3), P. 374–380.

12. Gleim A.V., Egorov V.I., Nazarov Y.V., Smirnov S.V., Chistyakov V.V., Bannik O.I., Anisimov A.A., Kynev S.M., Ivanova A.E., Collins R.J., Kozlov S.A., and Buller G.S. Secure polarization-independent subcarrier quantum key distribution in optical fiber channel using bb84 protocol with a strong reference. Optics Express, 2016, 24(3), P. 2619–2633.

13. Pereira D., Almeida M., Facao M., Pinto A.N., and Silva N.A. Probabilistic shaped 128-apsk cv-qkd transmission system over optical fibres. Optics Letters, 2022, 47(15), P. 3948–3951.

14. Roumestan F., Ghazisaeidi A., Renaudier J., Vidarte L. T., Leverrier A., Diamanti E., and Grangier P. Shaped constellation continuous variable quantum key distribution: Concepts, methods and experimental validation. Journal of Lightwave Technology, 2024, 42(15), P. 5182–5189.

15. da Silva V.L., Dias M.A., Neto N.A.F., and Tacla A.B. From coherent communications to quantum security: Modern techniques in cv-qkd. Proceedings of the Conference ”2024 SBFoton International Optics and Photonics Conference (SBFoton IOPC)”, Salvador, Brazil, 2024, P. 1–5.

16. Qi B., Huang L.-L., Qian L., and Lo H.-K. Experimental study on the gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers. Physical Review A–Atomic, Molecular, and Optical Physics, 2007, 76(5), P. 052323.

17. Nasedkin B., Goncharov R., Morozova P., Filipov I., Chistiakov V., Samsonov E., and Egorov V. Quantum hacking on the technical implementation of continuous-variable quantum key distribution systems. Radiophysics and Quantum Electronics, 2025, 67(1), P. 23–37.


Review

For citations:


Filipov I.M., Goncharov R.K., Dashkov M.V., Bogdanova E.I., Zinovev A.V., Chistiakov V.V., Kiselev F.D. Heterodyne detection method of multimode states for subcarrier wave continuous variable quantum key distribution. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(6):778-784. https://doi.org/10.17586/2220-8054-2025-16-6-778-784

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ISSN 2220-8054 (Print)
ISSN 2305-7971 (Online)