najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2022-13-4-372-391najo-249Research ArticleСтатьиContinuous-variable quantum key distribution: security analysis with trusted hardware noise against general attacksGoncharovR. K.rkgoncharov@itmo.ruKiselevA. D.alexei.d.kiselev@gmail.comSamsonovE. O.eosamsonov@itmo.ruEgorovV. I.viegorov@itmo.ruITMO UniversityRussian Federation202206062025134372391Copyright © Goncharov R.K., Kiselev A.D., Samsonov E.O., Egorov V.I., 20252025Goncharov R.K., Kiselev A.D., Samsonov E.O., Egorov V.I.Goncharov R.K., Kiselev A.D., Samsonov E.O., Egorov V.I.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/249

In this paper, using the full security framework for continuous-variable quantum key distribution (CV-QKD), we provide a composable security proof for the CV-QKD system in a realistic implementation. We take into account equipment losses and contributions from various components of excess noise and evaluate performance against collective and coherent attacks assuming trusted hardware noise. The calculation showed that the system remains operable at channel losses up to 10.2 dB in the presence of collective attacks and up to 7.5 dB in the presence of coherent ones.

quantum key distributioncontinuous variablessecurity proofcomposabilitytrusted noiseReferencesPirandola 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, P. 1012.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, P. 1012.Bennett C.H., Brassard G., Quantum cryptography: Public key distribution and coin tossing. Theoretical Computer Science, 2014, 560(12), P. 7-11.Bennett C.H., Brassard G., Quantum cryptography: Public key distribution and coin tossing. Theoretical Computer Science, 2014, 560(12), P. 7-11.Bennett C.H., Brassard G., Mermin N.D., Quantum cryptography without Bell’s theorem. Physical Review Letters, 1992, 68(2), P. 557-559.Bennett C.H., Brassard G., Mermin N.D., Quantum cryptography without Bell’s theorem. Physical Review Letters, 1992, 68(2), P. 557-559.Ralph T.C., Continuous variable quantum cryptography. Phys. Rev. A, 1999, 61(1), P. 010303.Ralph T.C., Continuous variable quantum cryptography. Phys. Rev. A, 1999, 61(1), P. 010303.Cerf N.J., Le´vy M., Assche G.V., Quantum distribution of Gaussian keys using squeezed states. Physical Review A, 2001, 63(4), P. 052311.Cerf N.J., Le´vy M., Assche G.V., Quantum distribution of Gaussian keys using squeezed states. Physical Review A, 2001, 63(4), P. 052311.Grosshans F., Van Assche G., Wenger J., Brouri R., Cerf N.J., Grangier P., Quantum key distribution using gaussian-modulated coherent states. Nature, 2003, 421(1), P. 238-241.Grosshans F., Van Assche G., Wenger J., Brouri R., Cerf N.J., Grangier P., Quantum key distribution using gaussian-modulated coherent states. Nature, 2003, 421(1), P. 238-241.Leverrier A., Grosshans F., Grangier P., Finite-size analysis of a continuous-variable quantum key distribution. Physical Review A, 2010, 81(6), P. 062343.Leverrier A., Grosshans F., Grangier P., Finite-size analysis of a continuous-variable quantum key distribution. Physical Review A, 2010, 81(6), P. 062343.Leverrier A., Composable Security Proof for Continuous-Variable Quantum Key Distribution with Coherent States. Physical Review Letters, 2015, 114(2), P. 070501.Leverrier A., Composable Security Proof for Continuous-Variable Quantum Key Distribution with Coherent States. Physical Review Letters, 2015, 114(2), P. 070501.Ghorai S.,Grangier P.,Diamanti E., and Leverrier A., Asymptotic Security of Continuous-Variable Quantum Key Distribution with a Discrete Modulation. Physical Review X, 2019, 9(6), P. 021059.Ghorai S.,Grangier P.,Diamanti E., and Leverrier A., Asymptotic Security of Continuous-Variable Quantum Key Distribution with a Discrete Modulation. Physical Review X, 2019, 9(6), P. 021059.Lin J., Upadhyaya T., Lu¨tkenhaus N., Asymptotic Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution. Phys. Rev. X, 2019, 9(12).Lin J., Upadhyaya T., Lu¨tkenhaus N., Asymptotic Security Analysis of Discrete-Modulated Continuous-Variable Quantum Key Distribution. Phys. Rev. X, 2019, 9(12).Denys A., Brown P., Leverrier A., Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation. Quantum, 2021, 5(9), P. 540.Denys A., Brown P., Leverrier A., Explicit asymptotic secret key rate of continuous-variable quantum key distribution with an arbitrary modulation. Quantum, 2021, 5(9), P. 540.Usenko V., Filip R., Trusted Noise in Continuous-Variable Quantum Key Distribution: A Threat and a Defense. Entropy, 2016, 18(1), P. 20.Usenko V., Filip R., Trusted Noise in Continuous-Variable Quantum Key Distribution: A Threat and a Defense. Entropy, 2016, 18(1), P. 20.Laudenbach F., Pacher C., Fung C.-H. F., Poppe A., Peev M., Schrenk B., Hentschel M., Walther P., and Hubel H., Continuous-Variable Quantum Key Distribution with Gaussian Modulation-The Theory of Practical Implementations. Advanced Quantum Technologies, 2018, 1(8), P. 1800011.Laudenbach F., Pacher C., Fung C.-H. F., Poppe A., Peev M., Schrenk B., Hentschel M., Walther P., and Hubel H., Continuous-Variable Quantum Key Distribution with Gaussian Modulation-The Theory of Practical Implementations. Advanced Quantum Technologies, 2018, 1(8), P. 1800011.Laudenbach F., Pacher C., Analysis of the Trusted-Device Scenario in Continuous-Variable Quantum Key Distribution. Advanced Quantum Technologies, 2019, 2(11), P. 1900055.Laudenbach F., Pacher C., Analysis of the Trusted-Device Scenario in Continuous-Variable Quantum Key Distribution. Advanced Quantum Technologies, 2019, 2(11), P. 1900055.Weedbrook C., Lance A.M., Bowen W.P., Symul T., Ralph T.C., Lam P.K., Quantum Cryptography Without Switching. Physical Review Letters, 2004, 93(10), P. 170504.Weedbrook C., Lance A.M., Bowen W.P., Symul T., Ralph T.C., Lam P.K., Quantum Cryptography Without Switching. Physical Review Letters, 2004, 93(10), P. 170504.Huang D., Huang P., Lin D., and Zeng G., Long-distance continuous-variable quantum key distribution by controlling excess noise. Scientific Reports, 2016, 6(5), P. 19201.Huang D., Huang P., Lin D., and Zeng G., Long-distance continuous-variable quantum key distribution by controlling excess noise. Scientific Reports, 2016, 6(5), P. 19201.Bennett C.H., Quantum cryptography using any two nonorthogonal states. Physical Review Letters, 1992, 68(5), P. 3121-3124.Bennett C.H., Quantum cryptography using any two nonorthogonal states. Physical Review Letters, 1992, 68(5), P. 3121-3124.Carter J., Wegman M.N., Universal classes of hash functions. Journal of Computer and System Sciences, 1979, 18(4), P. 143-154.Carter J., Wegman M.N., Universal classes of hash functions. Journal of Computer and System Sciences, 1979, 18(4), P. 143-154.Scarani V., Bechmann-Pasquinucci H., Cerf N.J., Du M.ifmmode checkselse sˇfiek, N. Lu¨tkenhaus, and M. Peev, The security of practical quantum key distribution. Reviews of Modern Physics, 2009, 81(9), P. 1301-1350.Scarani V., Bechmann-Pasquinucci H., Cerf N.J., Du M.ifmmode checkselse sˇfiek, N. Lu¨tkenhaus, and M. Peev, The security of practical quantum key distribution. Reviews of Modern Physics, 2009, 81(9), P. 1301-1350.Jouguet P., Kunz-Jacques S., Diamanti E., and Leverrier A., Analysis of imperfections in practical continuous-variable quantum key distribution, Physical Review A, 2012, 86(9), P. 032309.Jouguet P., Kunz-Jacques S., Diamanti E., and Leverrier A., Analysis of imperfections in practical continuous-variable quantum key distribution, Physical Review A, 2012, 86(9), P. 032309.Filip R., Continuous-variable quantum key distribution with noisy coherent states. Physical Review A, 2008, 77(2), P. 22310.Filip R., Continuous-variable quantum key distribution with noisy coherent states. Physical Review A, 2008, 77(2), P. 22310.Usenko V.C., Filip R., Feasibility of continuous-variable quantum key distribution with noisy coherent states. Physical Review A, 2010, 81(2), P. 022318.Usenko V.C., Filip R., Feasibility of continuous-variable quantum key distribution with noisy coherent states. Physical Review A, 2010, 81(2), P. 022318.Jacobsen C., Gehring T., and Andersen U., Continuous Variable Quantum Key Distribution with a Noisy Laser. Entropy, 2015, 17(7), P. 4654-4663.Jacobsen C., Gehring T., and Andersen U., Continuous Variable Quantum Key Distribution with a Noisy Laser. Entropy, 2015, 17(7), P. 4654-4663.Zhang Y., Chen Z., Pirandola S., Wang X., Zhou C., Chu B., Zhao Y., Xu B., Yu S., and Guo H., Long-Distance Continuous-Variable Quantum Key Distribution over 202.81 km of Fiber, Physical Review Letters, 2020, 125(6), P. 010502.Zhang Y., Chen Z., Pirandola S., Wang X., Zhou C., Chu B., Zhao Y., Xu B., Yu S., and Guo H., Long-Distance Continuous-Variable Quantum Key Distribution over 202.81 km of Fiber, Physical Review Letters, 2020, 125(6), P. 010502.Hosseinidehaj N., Lance A.M., Symul T., Walk N., and Ralph T.C., Finite-size effects in continuous-variable quantum key distribution with Gaussian postselection. Physical Review A, 2020, 101(5), P. 052335.Hosseinidehaj N., Lance A.M., Symul T., Walk N., and Ralph T.C., Finite-size effects in continuous-variable quantum key distribution with Gaussian postselection. Physical Review A, 2020, 101(5), P. 052335.Jouguet P., Kunz-Jacques S., Leverrier A., Grangier P., and Diamanti E., Experimental demonstration of long-distance continuous-variable quantum key distribution. Nature Photonics, 2013, 7(5), P. 378-381.Jouguet P., Kunz-Jacques S., Leverrier A., Grangier P., and Diamanti E., Experimental demonstration of long-distance continuous-variable quantum key distribution. Nature Photonics, 2013, 7(5), P. 378-381.Agrawal G.P., Fiber-optic communication systems, vol. 222. John Wiley & Sons, 2012.Agrawal G.P., Fiber-optic communication systems, vol. 222. John Wiley & Sons, 2012.Polarization Insensitive Isolator (ISO) http://www.lightcomm.com/product/view/typeid/235/id/268.html.Polarization Insensitive Isolator (ISO) http://www.lightcomm.com/product/view/typeid/235/id/268.html.Polarization Maintaining Fused Standard Coupler (PMC) http://www.lightcomm.com/home/product/view/typeid/189/id/206.html.Polarization Maintaining Fused Standard Coupler (PMC) http://www.lightcomm.com/home/product/view/typeid/189/id/206.html.Intensity Modulators https://photonics.ixblue.com/store/lithium-niobate-electro-optic-modulator/intensity-modulators.Intensity Modulators https://photonics.ixblue.com/store/lithium-niobate-electro-optic-modulator/intensity-modulators.Phase Modulators https://photonics.ixblue.com/store/lithium-niobate-electro-optic-modulator/phase-modulators.Phase Modulators https://photonics.ixblue.com/store/lithium-niobate-electro-optic-modulator/phase-modulators.Polarization Beam Combiner/Splitter (PBC/PBS) http://www.lightcomm.com/product/view/typeid/190/id/212.html.Polarization Beam Combiner/Splitter (PBC/PBS) http://www.lightcomm.com/product/view/typeid/190/id/212.html.-Degree Optical Hybrid http://www.optoplex.com/Optical_Hybrid.htm.-Degree Optical Hybrid http://www.optoplex.com/Optical_Hybrid.htm.Polarization Maintaining Isolator (PMISO) http://www.lightcomm.com/product/view/typeid/190/id/211.html.Polarization Maintaining Isolator (PMISO) http://www.lightcomm.com/product/view/typeid/190/id/211.html.HIGH SPEED POLARIZATION CONTROLLER-SCRAMBLER (OEM VERSION) https://www.ozoptics.com/ALLNEW PDF/DTS0143.pdf.HIGH SPEED POLARIZATION CONTROLLER-SCRAMBLER (OEM VERSION) https://www.ozoptics.com/ALLNEW PDF/DTS0143.pdf.Hosseinidehaj N., Walk N., and Ralph T.C., Optimal realistic attacks in continuous-variable quantum key distribution. Physical Review A, 2019, 99(5), P. 1-11.Hosseinidehaj N., Walk N., and Ralph T.C., Optimal realistic attacks in continuous-variable quantum key distribution. Physical Review A, 2019, 99(5), P. 1-11.Pirandola S., Limits and security of free-space quantum communications. Physical Review Research, 2021, 3(3), P. 013279.Pirandola S., Limits and security of free-space quantum communications. Physical Review Research, 2021, 3(3), P. 013279.Pirandola S., Composable security for continuous variable quantum key distribution: Trust levels and practical key rates in wired and wireless networks. Physical Review Research, 2021, 3(10), P. 043014.Pirandola S., Composable security for continuous variable quantum key distribution: Trust levels and practical key rates in wired and wireless networks. Physical Review Research, 2021, 3(10), P. 043014.Qi B., Lougovski P., Pooser R., Grice W., and Bobrek M., Generating the Local Oscillator “Locally” in Continuous-Variable Quantum Key Distribution Based on Coherent Detection. Physical Review X, 2015, 5(10), P. 041009.Qi B., Lougovski P., Pooser R., Grice W., and Bobrek M., Generating the Local Oscillator “Locally” in Continuous-Variable Quantum Key Distribution Based on Coherent Detection. Physical Review X, 2015, 5(10), P. 041009.Soh D.B., Brif C., Coles P.J., Lutkenhaus N., Camacho R.M., Urayama J., and Sarovar M., Self-referenced continuous-variable quantum key distribution protocol. Physical Review X, 2015, 5(4), P. 1-15.Soh D.B., Brif C., Coles P.J., Lutkenhaus N., Camacho R.M., Urayama J., and Sarovar M., Self-referenced continuous-variable quantum key distribution protocol. Physical Review X, 2015, 5(4), P. 1-15.Kleis S., Rueckmann M., and Schaeffer C.G., Continuous variable quantum key distribution with a real local oscillator using simultaneous pilot signals. Optics Letters, 2017, 42(4), P. 1588.Kleis S., Rueckmann M., and Schaeffer C.G., Continuous variable quantum key distribution with a real local oscillator using simultaneous pilot signals. Optics Letters, 2017, 42(4), P. 1588.Laudenbach F., Schrenk B., Pacher C., Hentschel M., Fung C.-H.F., Karinou F., Poppe A., Peev M., and Hubel H., Pilot-assisted intradyne reception for high-speed continuous-variable quantum key distribution with true local oscillator. Quantum, 2019, 3(10), P. 193.Laudenbach F., Schrenk B., Pacher C., Hentschel M., Fung C.-H.F., Karinou F., Poppe A., Peev M., and Hubel H., Pilot-assisted intradyne reception for high-speed continuous-variable quantum key distribution with true local oscillator. Quantum, 2019, 3(10), P. 193.Szynowski J., CMRR analysis of instrumentation amplifiers. Electronics Letters, 1983, 19(14), P. 547.Szynowski J., CMRR analysis of instrumentation amplifiers. Electronics Letters, 1983, 19(14), P. 547.Tang X., Kumar R., Ren S., Wonfor A., Penty R., and White I., Performance of continuous variable quantum key distribution system at different detector bandwidth. Optics Communications, 2020, 471(9), P. 126034.Tang X., Kumar R., Ren S., Wonfor A., Penty R., and White I., Performance of continuous variable quantum key distribution system at different detector bandwidth. Optics Communications, 2020, 471(9), P. 126034.Devetak I. and Winter A., Distillation of secret key and entanglement from quantum states, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005, 461(1), P. 207-235.Devetak I. and Winter A., Distillation of secret key and entanglement from quantum states, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2005, 461(1), P. 207-235.Tomamichel M., Colbeck R., and Renner R., A fully quantum asymptotic equipartition property. IEEE Transactions on information theory, 2009, 55(12), P. 5840-5847.Tomamichel M., Colbeck R., and Renner R., A fully quantum asymptotic equipartition property. IEEE Transactions on information theory, 2009, 55(12), P. 5840-5847.Tomamichel M., Schaffner C., Smith A., and Renner R., Leftover Hashing Against Quantum Side Information. IEEE Transactions on Information Theory, 2011, 57(8), P. 5524-5535.Tomamichel M., Schaffner C., Smith A., and Renner R., Leftover Hashing Against Quantum Side Information. IEEE Transactions on Information Theory, 2011, 57(8), P. 5524-5535.Tomamichel M., Quantum Information Processing with Finite Resources. Cham: Springer International Publishing, 2016.Tomamichel M., Quantum Information Processing with Finite Resources. Cham: Springer International Publishing, 2016.Leverrier A., Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction. Physical Review Letters, 2017, 118(5), P. 200501.Leverrier A., Security of Continuous-Variable Quantum Key Distribution via a Gaussian de Finetti Reduction. Physical Review Letters, 2017, 118(5), P. 200501.Van Assche G., Cardinal J., and Cerf N., Reconciliation of a Quantum-Distributed Gaussian Key. IEEE Transactions on Information Theory, 2004, 50(2), P. 394-400.Van Assche G., Cardinal J., and Cerf N., Reconciliation of a Quantum-Distributed Gaussian Key. IEEE Transactions on Information Theory, 2004, 50(2), P. 394-400.Mani H., Error Reconciliation Protocols for Continuous-Variable Quantum Key Distribution. PhD thesis, Technical University of Denmark, 2021.Mani H., Error Reconciliation Protocols for Continuous-Variable Quantum Key Distribution. PhD thesis, Technical University of Denmark, 2021.Wen X., Li Q., Mao H., Wen X., and Chen N., Rotation Based Slice Error Correction Protocol for Continuous-variable Quantum Key Distribution and its Implementation with Polar Codes. arXiv preprint arXiv:2106.06206, 2021, 6, P. 1-17.Wen X., Li Q., Mao H., Wen X., and Chen N., Rotation Based Slice Error Correction Protocol for Continuous-variable Quantum Key Distribution and its Implementation with Polar Codes. arXiv preprint arXiv:2106.06206, 2021, 6, P. 1-17.

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