najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2023-14-2-178-185najo-128Research ArticlePHYSICSФИЗИКАTheoretical study of the EDFA optical amplifier implementation scheme improving the performance of a quantum key distribution system integrated with an WDM optical transport networkТеоретическое исследование схемы использования оптического усилителя EDFA, улучшающей производительность системы распределения квантовых ключей, интегрированной в оптическую транспортную сеть с применением технологии WDMhttps://orcid.org/0000-0002-8804-6569ТупяковД. В.TupyakovD.

Daniil Tupyakov

Kronverkskiy, 49, St. Petersburg, 197101

dvtupiakov@itmo.ruhttps://orcid.org/0000-0002-2024-9773ИванковН. А.IvankovN.

Nikita Ivankov

Kronverkskiy, 49, St. Petersburg, 197101

ivankov.nikita2014@gmail.comhttps://orcid.org/0000-0001-9861-0816ВоронцоваИ. О.VorontsovaI. V.

Irina Vorontsova

Kronverkskiy, 49, St. Petersburg, 197101

iovorontsova@itmo.ruhttps://orcid.org/0000-0002-3894-511XКиселёвФ. Д.KiselevF.

Fedor Kiselev

Kronverkskiy, 49, St. Petersburg, 197101

fdkiselev@itmo.ruhttps://orcid.org/0000-0003-0767-0261ЕгоровВ. И.EgorovV.

Vladimir Egorov

Kronverkskiy, 49, St. Petersburg, 197101

viegorov@itmo.ruITMO UniversityRussian Federation202303062025142178185Copyright © Tupyakov D., Ivankov N., Vorontsova I.V., Kiselev F., Egorov V., 20252025Тупяков Д.В., Иванков Н.А., Воронцова И.О., Киселёв Ф.Д., Егоров В.И.Tupyakov D., Ivankov N., Vorontsova I.V., Kiselev F., Egorov V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/128

A version of an erbium doped fiber amplifier (EDFA) application scheme designed to increase the efficiency of the simultaneous quantum key distribution session and transmission of information by classical channels in a single optical fiber is explored. A theoretical study of the possibility to use EDFA in the explored way was conducted by numerical simulation methods. The mathematical model is based on the EDFA dynam ics equations and the equations that determine the secure key generation rate in case of the subcarrier-wave quantum key distribution. A method for determining the optimal parameters of the scheme under study is de scribed and the evaluation of the feasibility of using EDFA in the explored way is performed. A comparative analysis of the subcarrier-wave quantum key distribution system performance when integrated into an optical network is made in terms of the secure key generation rate for the cases when EDFA is either used or not. The results obtained demonstrate high efficiency of the scheme under study, i.e., the maximum achievable distance of the secure key distribution is increased while maintaining the efficiency of the information transmission.

Исследуется вариант схемы применения волоконно – оптического усилителя (EDFA) на основе волокна, легированного ионами эрбия, предназначенный для повышения эффективности сеанса распределения квантового ключа и передачи информации по классическим каналам проводимых одновременно в одном оптическом волокне. Методами численного моделирования проведено теоретическое исследование возможности использования EDFA исследуемым способом. Математическая модель основана на уравнениях динамики EDFA и уравнениях, определяющих скорость генерации секретного ключа в случае распределения квантового ключа на боковых частотах. Описан метод определения оптимальных параметров исследуемой схемы и проведена оценка целесообразности использования EDFA исследуемым способом. Проведен сравнительный анализ производительности системы распределения квантовых ключей на боковых частотах при интеграции в оптическую сеть с точки зрения скорости генерации защищенного ключа для случаев, когда EDFA либо используется, либо нет. Полученные результаты демонстрируют высокую эффективность исследуемой схемы, т.е. увеличивается максимально достижимая дальность безопасного распределения ключей при сохранении эффективности передачи информации.

усилитель на эрбиевом волокнеEDFAквантовое распределение ключабоковые частотыerbium-doped fiber amplifierquantum key distributionsubcarrier-wave quantum key distributionThe work was done by Leading Research Center “National Center for Quantum Inter net” of ITMO University by the order of JSCo Russian RailwaysReferencesScarani V., Bechmann-Pasquinucci H., Cerf J.N., Duˇ sek M., L¨utkenhaus N., Peev M. The security of practical quantum key distribution. Reviews of Modern Physics, 2009, 81 (3), P. 1301–1350.Scarani V., Bechmann-Pasquinucci H., Cerf J.N., Duˇ sek M., L¨utkenhaus N., Peev M. The security of practical quantum key distribution. Reviews of Modern Physics, 2009, 81 (3), P. 1301–1350.Pirandola S., Andersen U.L., Banchi L., Berta M., Bunandar D., Colbeck R., Englund D., GehringT., LupoC., Ottaviani C., Pereira J.L., Razavi M., Shamsul Shaari J., Tomamichel M., Usenko V.C., Vallone G., Villoresi P., Wallden P. Advances in quantum cryptography. Advances in Optics and Photonics, 2020, 12 (4), 1012.Pirandola S., Andersen U.L., Banchi L., Berta M., Bunandar D., Colbeck R., Englund D., GehringT., LupoC., Ottaviani C., Pereira J.L., Razavi M., Shamsul Shaari J., Tomamichel M., Usenko V.C., Vallone G., Villoresi P., Wallden P. Advances in quantum cryptography. Advances in Optics and Photonics, 2020, 12 (4), 1012.Gisin N., Ribordy G., Tittel W., Zbinden H. Quantum cryptography. Reviews of Modern Physics, 2002, 74 (1), P. 145–196.Gisin N., Ribordy G., Tittel W., Zbinden H. Quantum cryptography. Reviews of Modern Physics, 2002, 74 (1), P. 145–196.Mlejnek M., Kaliteevskiy N., Nolan D.A. Reducing spontaneous Raman scattering noise in high quantum bit rate QKD systems over optical fiber. 2017, URL: https://arxiv.org/ftp/arxiv/papers/1712/1712.05891.pdf.Mlejnek M., Kaliteevskiy N., Nolan D.A. Reducing spontaneous Raman scattering noise in high quantum bit rate QKD systems over optical fiber. 2017, URL: https://arxiv.org/ftp/arxiv/papers/1712/1712.05891.pdf.Niu J.-N., Sun Y.-M., Cai C., Ji-Y.-F. Optimized channel allocation scheme for jointly reducing four-wave mixing and Raman scattering in the DWDM-QKDsystem. Applied Optics, 2018, 57 (27), 7987.Niu J.-N., Sun Y.-M., Cai C., Ji-Y.-F. Optimized channel allocation scheme for jointly reducing four-wave mixing and Raman scattering in the DWDM-QKDsystem. Applied Optics, 2018, 57 (27), 7987.Kumar R., Qin H., All´eaume R. Coexistence of continuous variable QKD with intense DWDM classical channels. New J. of Physics, 2015, 17, 043027.Kumar R., Qin H., All´eaume R. Coexistence of continuous variable QKD with intense DWDM classical channels. New J. of Physics, 2015, 17, 043027.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., et al. 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.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., et al. 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.Merolla J., Mazurenko Y., Goedgebuer J.P. Quantum Gryptography using Frequency Modulation of Weak Ligh Pulses. Proceedings of European Quantum Electronics Conference. Glasgow, UK, Technical Digest of EQEC 1998, 1998, 101.Merolla J., Mazurenko Y., Goedgebuer J.P. Quantum Gryptography using Frequency Modulation of Weak Ligh Pulses. Proceedings of European Quantum Electronics Conference. Glasgow, UK, Technical Digest of EQEC 1998, 1998, 101.Choi I., Zhou Y.R., F.-Dynes J., Yuan Z., Klar A., Sharpe A., Plews A., Lucamarini M., Radig C., Neubert J., Griesser H., Eiselt M., Chunnilall C., Lepert G., Sinclair A., Elbers Z.-P., Lord A., Shields A. Field trial of a quantum secured 10 Gb/s DWDM transmission system over a single installed fiber. Optics Express, 2014, 22 (19), 23121.Choi I., Zhou Y.R., F.-Dynes J., Yuan Z., Klar A., Sharpe A., Plews A., Lucamarini M., Radig C., Neubert J., Griesser H., Eiselt M., Chunnilall C., Lepert G., Sinclair A., Elbers Z.-P., Lord A., Shields A. Field trial of a quantum secured 10 Gb/s DWDM transmission system over a single installed fiber. Optics Express, 2014, 22 (19), 23121.Sharma R., Raghuwanshi S.K. Computer Model for EDFA Dynamics Over 1525-1560nm Band Using a Novel Multi-Wavelength MATLAB Simulink Test Bed for 8-Channels. IETE J. of Research, 2018, 64 (6), P. 814–831.Sharma R., Raghuwanshi S.K. Computer Model for EDFA Dynamics Over 1525-1560nm Band Using a Novel Multi-Wavelength MATLAB Simulink Test Bed for 8-Channels. IETE J. of Research, 2018, 64 (6), P. 814–831.Pinter S., Jean J., Fernando X. A dynamic multi-wavelength simulink model for EDFA. Proceedings of Canadian Conference on Electrical and Computer Engineering 2004, Niagara Falls, Ontario, Canada, IEEE, 2004, P. 2077–2080.Pinter S., Jean J., Fernando X. A dynamic multi-wavelength simulink model for EDFA. Proceedings of Canadian Conference on Electrical and Computer Engineering 2004, Niagara Falls, Ontario, Canada, IEEE, 2004, P. 2077–2080.Giles C.R., Desurvire E. Modeling erbium-doped fiber amplifiers. J. of Lightwave Technology, 1991, 9 (2), P. 271–283.Giles C.R., Desurvire E. Modeling erbium-doped fiber amplifiers. J. of Lightwave Technology, 1991, 9 (2), P. 271–283.Lebedev V.F., Serduk K.V., Fomenko I.N. Laser Technology. St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, 2021, 45 p.Lebedev V.F., Serduk K.V., Fomenko I.N. Laser Technology. St. Petersburg State University of Aerospace Instrumentation, St. Petersburg, 2021, 45 p.Kiselev F., Veselkova N., Goncharov R., Egorov V. A theoretical study of subcarrier-wave quantum key distribution system integration with an optical transport network utilizing dense wavelength division multiplexing. J. of Physics B: Atomic, Molecular and Optical Physics, 2021, 54 (13), 135502.Kiselev F., Veselkova N., Goncharov R., Egorov V. A theoretical study of subcarrier-wave quantum key distribution system integration with an optical transport network utilizing dense wavelength division multiplexing. J. of Physics B: Atomic, Molecular and Optical Physics, 2021, 54 (13), 135502.Pradhan D., Vivekanand M. Analysis and Review of EDFA. Int. J. of Computer Science and Network, 2015, 4 (6), P. 918–923.Pradhan D., Vivekanand M. Analysis and Review of EDFA. Int. J. of Computer Science and Network, 2015, 4 (6), P. 918–923.

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