najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2021-12-2-161-166najo-354Research ArticlePHYSICSФИЗИКАHeterodyne-based subcarrier wave quantum cryptography under the chromatic dispersion impactВлияние хроматической дисперсии на систему квантовой криптографии на боковых частотах с гетеродинным методом детектированияГончаровРоман К.GoncharovR. K.

Kronverkskiy, 49, St. Petersburg, 197101

Kronverkskiy, 49, St. Petersburg, 197101

rkgoncharov@itmo.ruЗиновьевАлександр В.ZinovevA. V.

Kronverkskiy, 49, St. Petersburg, 197101

Kronverkskiy, 49, St. Petersburg, 197101

КиселевФедор Д.KiselevF. D.

Kronverkskiy, 49, St. Petersburg, 197101,

Vasilievsky island, 6 Line, 59, St. Petersburg, 199178

Kronverkskiy, 49, St. Petersburg, 197101,

Vasilievsky island, 6 Line, 59, St. Petersburg, 199178

СамсоновЭдуард О.SamsonovE. O.

Kronverkskiy, 49, St. Petersburg, 197101,

Vasilievsky island, 6 Line, 59, St. Petersburg, 199178

Kronverkskiy, 49, St. Petersburg, 197101,

Vasilievsky island, 6 Line, 59, St. Petersburg, 199178

eosamsonov@itmo.ruSt. Petersburg National Research ITMO UniversitySt. Petersburg National Research ITMO UniversitySt. Petersburg National Research ITMO University; Quanttelecom LLCSt. Petersburg National Research ITMO University; Quanttelecom LLC202128072025122161166Copyright © Goncharov R.K., Zinovev A.V., Kiselev F.D., Samsonov E.O., 20252025Гончаров Р.К., Зиновьев А.В., Киселев Ф.Д., Самсонов Э.О.Goncharov R.K., Zinovev A.V., Kiselev F.D., Samsonov E.O.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/354

In this paper, we investigate the effect of chromatic dispersion on a continuous variable quantum key distribution system with heterodyne detection, in which information is encoded in the sidebands of modulated laser radiation. We consider the system in which a balanced detector output is downconverted to an intermediate frequency and propose a non-standard methods of dispersion compensation using RF phase shifters.

В настоящей работе исследуется влияние хроматической дисперсии на систему квантового распределения ключей на непрерывных переменных с гетеродинным методом детектирования, где информация кодируется в боковых частотных модах модулированного лазерного излучения. Рассмотрена система, в которой отклик балансного детектора наблюдается на промежуточной частоте, и предложены нестандартные методы компенсации дисперсии с помощью радиочастотных фазовращателей. 

гетеродинное детектированиебоковые частотыквантовое распределение ключейхроматическая дисперсияheterodyne detectionsubcarrier wavequantum key distributionchromatic dispersionReferencesPirandola S., Andersen U.L., et al. Advances in quantum cryptography. Advances in Optics and Photonics, 2020, 12 (4), P. 1012–1236.Pirandola S., Andersen U.L., et al. Advances in quantum cryptography. Advances in Optics and Photonics, 2020, 12 (4), P. 1012–1236.Bennett C., Brassard G. Quantum cryptography: public key distribution and coin tossing. Proceedings of “IEEE International Conference on Computers, Systems and Signal”, Bangalore, India, IEEE, 1984, P. 175–179.Bennett C., Brassard G. Quantum cryptography: public key distribution and coin tossing. Proceedings of “IEEE International Conference on Computers, Systems and Signal”, Bangalore, India, IEEE, 1984, P. 175–179.Lo H.-K., Curty M., Tamaki K. Secure quantum key distribution. Nature Photonics, 2014, 8 (8), P. 595–604.Lo H.-K., Curty M., Tamaki K. Secure quantum key distribution. Nature Photonics, 2014, 8 (8), P. 595–604.Ralph T.C. Continuous variable quantum cryptography. Physical Review A, 1999, 61 (1), 010303.Ralph T.C. Continuous variable quantum cryptography. Physical Review A, 1999, 61 (1), 010303.Grosshans F., Van Assche G., et al. Quantum key distribution using gaussian-modulated coherent states. Nature, 2003, 421 (6920), P. 238–241.Grosshans F., Van Assche G., et al. Quantum key distribution using gaussian-modulated coherent states. Nature, 2003, 421 (6920), P. 238–241.Hirano T., Yamanaka H., et al. Quantum cryptography using pulsed homodyne detection. Physical Review A, 2003, 68 (4), 042331.Hirano T., Yamanaka H., et al. Quantum cryptography using pulsed homodyne detection. Physical Review A, 2003, 68 (4), 042331.Leverrier A., Grangier P. Continuous-variable quantum-key-distribution protocols with a non-gaussian modulation. Physical Review A, 2011, 83 (4), 042312.Leverrier A., Grangier P. Continuous-variable quantum-key-distribution protocols with a non-gaussian modulation. Physical Review A, 2011, 83 (4), 042312.Heid M., Lutkenhaus N. Efficiency of coherent-state quantum cryptography in the presence of loss: Influence of realistic error correction. ¨ Physical Review A, 2006, 73 (5), 052316.Heid M., Lutkenhaus N. Efficiency of coherent-state quantum cryptography in the presence of loss: Influence of realistic error correction. ¨ Physical Review A, 2006, 73 (5), 052316.Bradler K., Weedbrook C. Security proof of continuous-variable quantum key distribution using three coherent states. ´ Physical Review A, 2018, 97 (2), 022310.Bradler K., Weedbrook C. Security proof of continuous-variable quantum key distribution using three coherent states. ´ Physical Review A, 2018, 97 (2), 022310.Papanastasiou P., Lupo C. , Weedbrook C. , Pirandola S. Quantum key distribution with phase-encoded coherent states: Asymptotic security analysis in thermal-loss channels. Physical Review A, 2018, 98 (1), 012340.Papanastasiou P., Lupo C. , Weedbrook C. , Pirandola S. Quantum key distribution with phase-encoded coherent states: Asymptotic security analysis in thermal-loss channels. Physical Review A, 2018, 98 (1), 012340.Lin J., Upadhyaya T., Lutkenhaus N. Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. ¨ Physical Review X, 2019, 9 (4), 041064.Lin J., Upadhyaya T., Lutkenhaus N. Asymptotic security analysis of discrete-modulated continuous-variable quantum key distribution. ¨ Physical Review X, 2019, 9 (4), 041064.Comandar L.C., Brunner H.H., et al. A flexible continuous-variable QKD system using off-the-shelf components. Quantum Information Science and Technology III, 2018, 10442, P. 37–43.Comandar L.C., Brunner H.H., et al. A flexible continuous-variable QKD system using off-the-shelf components. Quantum Information Science and Technology III, 2018, 10442, P. 37–43.Wang H., Pi Y., et al. High-speed gaussian-modulated continuous-variable quantum key distribution with a local oscillator based on pilot-toneassisted phase compensation. Optics Express, 2020, 28 (22), P. 32882–32893.Wang H., Pi Y., et al. High-speed gaussian-modulated continuous-variable quantum key distribution with a local oscillator based on pilot-toneassisted phase compensation. Optics Express, 2020, 28 (22), P. 32882–32893.Fossier S., Diamanti E., et al. Field test of a continuous-variable quantum key distribution prototype. New Journal of Physics, 2009, 11 (4), 045023.Fossier S., Diamanti E., et al. Field test of a continuous-variable quantum key distribution prototype. New Journal of Physics, 2009, 11 (4), 045023.Gleim A.V., Egorov V.I., 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. 2619–2619.Gleim A.V., Egorov V.I., 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. 2619–2619.Miroshnichenko G.P., Kozubov A.V., et al. Security of subcarrier wave quantum key distribution against the collective beam-splitting attack. Optics Express, 2018, 26 (9), P. 11292–11308.Miroshnichenko G.P., Kozubov A.V., et al. Security of subcarrier wave quantum key distribution against the collective beam-splitting attack. Optics Express, 2018, 26 (9), P. 11292–11308.Kynev S.M., Chistyakov V.V., et al. Free-space subcarrier wave quantum communication. Journal of Physics: Conference Series, 2017, 917, 052003.Kynev S.M., Chistyakov V.V., et al. Free-space subcarrier wave quantum communication. Journal of Physics: Conference Series, 2017, 917, 052003.Merolla J.-M., Mazurenko Y., et al. Phase-modulation transmission system for quantum cryptography. Optics Letters, 1999, 24 (2), P. 104–106.Merolla J.-M., Mazurenko Y., et al. Phase-modulation transmission system for quantum cryptography. Optics Letters, 1999, 24 (2), P. 104–106.Chistiakov V., Kozubov A., et al. Feasibility of twin-field quantum key distribution based on multi-mode coherent phase-coded states. Optics Express, 2019, 27 (25), P. 36551–36561.Chistiakov V., Kozubov A., et al. Feasibility of twin-field quantum key distribution based on multi-mode coherent phase-coded states. Optics Express, 2019, 27 (25), P. 36551–36561.Samsonov E., Goncharov R., et al. Subcarrier wave continuous variable quantum key distribution with discrete modulation: mathematical model and finite-key analysis. Scientific Reports, 2020, 10 (1), P. 1–9.Samsonov E., Goncharov R., et al. Subcarrier wave continuous variable quantum key distribution with discrete modulation: mathematical model and finite-key analysis. Scientific Reports, 2020, 10 (1), P. 1–9.Miroshnichenko G.P., Kiselev A.D., Trifanov A.I., Gleim A.V. Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model. Journal of the Optical Society of America B, 2017, 34 (6), P. 1177–1190.Miroshnichenko G.P., Kiselev A.D., Trifanov A.I., Gleim A.V. Algebraic approach to electro-optic modulation of light: exactly solvable multimode quantum model. Journal of the Optical Society of America B, 2017, 34 (6), P. 1177–1190.Capmany J., Fernandez-Pousa C.R. Quantum model for electro-optical phase modulation. ´ Journal of the Optical Society of America B, 2010, 27 (6), A119–A129.Capmany J., Fernandez-Pousa C.R. Quantum model for electro-optical phase modulation. ´ Journal of the Optical Society of America B, 2010, 27 (6), A119–A129.Kumar P., Prabhakar A. Evolution of quantum states in an electro-optic phase modulator. IEEE journal of quantum electronics, 2008, 45 (2), P. 149–156.Kumar P., Prabhakar A. Evolution of quantum states in an electro-optic phase modulator. IEEE journal of quantum electronics, 2008, 45 (2), P. 149–156.Samsonov E., Goncharov R., et al. Coherent detection schemes for subcarrier wave continuous variable quantum key distribution. ArXiv:2006.16543, 2020.Samsonov E., Goncharov R., et al. Coherent detection schemes for subcarrier wave continuous variable quantum key distribution. ArXiv:2006.16543, 2020.Kiselev F., Samsonov E., et al. Analysis of the chromatic dispersion effect on the subcarrier wave QKD system. Optics Express, 2020, 28 (19), P. 28696–28712.Kiselev F., Samsonov E., et al. Analysis of the chromatic dispersion effect on the subcarrier wave QKD system. Optics Express, 2020, 28 (19), P. 28696–28712.Kleis S., Rueckmann M., Schaeffer C.G. Continuous-variable quantum key distribution with a real local oscillator and without auxiliary signals. ArXiv:1908.03625, 2019.Kleis S., Rueckmann M., Schaeffer C.G. Continuous-variable quantum key distribution with a real local oscillator and without auxiliary signals. ArXiv:1908.03625, 2019.Huang D., Lin D.,et al. Continuous-variable quantum key distribution with 1 Mbps secure key rate. Optics Express, 2015, 23 (13), P. 17511– 17519.Huang D., Lin D.,et al. Continuous-variable quantum key distribution with 1 Mbps secure key rate. Optics Express, 2015, 23 (13), P. 17511– 17519.Agrawal G.P. Fiber-optic communication systems. John Wiley & Sons, Hoboken, 2012, 626 p.Agrawal G.P. Fiber-optic communication systems. John Wiley & Sons, Hoboken, 2012, 626 p.Horowitz P., Hill W. The art of electronics. Cambridge University Press, Cambridge, 1989, 1220 p.Horowitz P., Hill W. The art of electronics. Cambridge University Press, Cambridge, 1989, 1220 p.Xinyi T. Broadband phase shifter design for phased array radar systems. PhD Thesis, National University of Singapore, 2011.Xinyi T. Broadband phase shifter design for phased array radar systems. PhD Thesis, National University of Singapore, 2011.

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