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Enhancing the Unidimensional Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction

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Abstract

Unidimensional continuous-variable quantum key distribution (CV-QKD) protocol with Gaussian modulation is simpler in implementation and lower in costs than its two-dimensional counterpart, but its secure transmission distance is not as far as the latter. In this paper, we give a solution that using the photon subtraction, which is one of non-Gaussian operations, to improve the performance of the unidimensional CV-QKD protocol. Security analysis and numerical simulation indicate that the photon subtraction operation can significantly improve the secure transmission distance of the unidimensional CV-QKD protocol.

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References

  1. Braunstein, S.L., van Loock, P.: Quantum information with continuous variables. Rev. Mod. Phys. 77, 513 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  2. Weedbrook, C., Pirandola, S., García-Patrón, R., Cerf, N.J., Ralph, T.C., Shapiro, J.H., Lloyd, S.: Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)

    Article  ADS  Google Scholar 

  3. Jouguet, P., Elkouss, D., Kunz-Jacques, S.: High-bit-rate continuous-variable quantum key distribution. Phys. Rev. A 90, 042329 (2014)

    Article  ADS  Google Scholar 

  4. Zhang, G., Haw, J.Y., Cai, H., Xu, F., Assad, S.M., Fitzsimons, J.F., Zhou, X., Zhang, Y., Yu, S., Wu, J., Ser, W., Kwek, L.C., Liu, A.Q.: An integrated silicon photonic chip platform for continuous-variable quantum key distribution. Nat. Photonics 9, 1–4 (2019)

    Google Scholar 

  5. Huang, D., Huang, P., Lin, D.K., Zeng, G.H.: Long-distance continuous-variable quantum key distribution by controlling excess noise. Sci. Rep. 6, 19201 (2016)

    Article  ADS  Google Scholar 

  6. Jouguet, P., Kunz-Jacques, S., Leverrier, A., Grangier, P., Diamanti, E.: Experimental demonstration of long-distance continuous-variable quantum key distribution. Nat. Photonics 7, 378 (2013)

    Article  ADS  Google Scholar 

  7. Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)

    Article  ADS  Google Scholar 

  8. Grosshans, F., Van Assche, G., Wenger, J., Brouri, R., Cerf, N.J., Grangier, P.: Quantum key distribution using gaussian-modulated coherent states. Nature 421, 238 (2003)

    Article  ADS  Google Scholar 

  9. Weedbrook, C., Lance, A.M., Bowen, W.P., Symul, T., Ralph, T.C., Lam, P.K.: Quantum cryptography without switching. Phys. Rev. Lett. 93, 170504 (2004)

    Article  ADS  Google Scholar 

  10. Qi, B., Huang, L.L., Qian, L., Lo, H.K.: Experimental study on the Gaussian-modulated coherent-state quantum key distribution over standard telecommunication fibers. Phys. Rev. A 76, 052323 (2007)

    Article  ADS  Google Scholar 

  11. Zhang, Y.C., Li, Z.Y., Chen, Z.Y., Weedbrook, C., Zhao, Y.J., Wang, X.Y., Huang, Y.D., Xu, C.C., Zhang, X.X., Wang, Z.Y., Li, M., Zhang, X.Y., Zheng, Z.Y., Chu, B.J., Gao, X.Y., Meng, N., Cai, W.W., Wang, Z., Wang, G., Yu, S., Guo, H.: Continuous-variable QKD over 50 km commercial fiber. Quantum Sci. Technol. 4, 035006 (2019)

    Google Scholar 

  12. Usenko, V.C., Grosshans, F.: Unidimensional continuous-variable quantum key distribution. Phys. Rev. A 92, 062337 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  13. Gehring, T., Jacobsen, C.S., Andersen, U.L.: Single-quadrature continuous-variable quantum key distribution. Quantum Inf. Comput. 16, 1081 (2016)

    MathSciNet  Google Scholar 

  14. Usenko, V.C.: Unidimensional continuous-variable quantum key distribution using squeezed states. Phys. Rev. A 98, 032321 (2018)

    Article  ADS  Google Scholar 

  15. Wang, T.Y., Li, L., Li, M.: Unidimensional continuous-variable quantum key distribution with noisy source. Quantum Inf. Process. 19, 3 (2019)

    Google Scholar 

  16. Shen, S.Y., Bai, M.W., Zheng, X.T.: Free-space continuous-variable quantum key distribution of unidimensional Gaussian modulation using polarized coherent states in an urban environment. Phys. Rev. A 100, 012325 (2019)

    Article  ADS  Google Scholar 

  17. Zhao, W., Shi, R., Feng, Y.Y., Huang, D.: Unidimensional continuous-variable quantum key distribution with discrete modulation. Phys. Lett. A 384, 126061 (2020)

    Article  MathSciNet  Google Scholar 

  18. Wang, P., Wang, X.Y., Li, J.Q., Li, Y.M.: Finite-size analysis of unidimensional continuous-variable quantum key distribution under realistic conditions. Opt. Express 25, 27995 (2017)

    Article  ADS  Google Scholar 

  19. Wang, X.Y., Liu, W.Y., Wang, P., Li, Y.M.: Experimental study on all-fiber-based unidimensional continuous-variable quantum key distribution. Phys. Rev. A 95, 062330 (2017)

    Article  ADS  Google Scholar 

  20. Wang, P., Wang, X.Y., Li, Y.M.: Security analysis of unidimensional continuous-variable quantum key distribution using uncertainty relations. Entropy 20, 157 (2018)

    Article  ADS  Google Scholar 

  21. Huang, L.Y., Zhang, Y.C., Chen, Z.Y., Yu, S.: Unidimensional continuous-variable quantum key distribution with untrusted detection under realistic conditions. Entropy 21, 1100 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  22. Bai, D.Y., Huang, P., Zhu, Y.Q., Ma, H.X., Xiang, T.L., Wang, T., Zeng, G.H.: Unidimensional continuous-variable measurement-device-independent quantum key distribution. Quantum Inf Process. 19, 53 (2020)

    Article  ADS  Google Scholar 

  23. Huang, L.Y., Zhang, Y.C., Huang, Y.D., Jiang, T.W., Yu, S.: Improvement of unidimensional continuous-variable quantum key distribution systems by using a phase-sensitive amplifier. J. Phys. B:, At. Mol. Opt. Phys. 52, 225502 (2019)

    Article  ADS  Google Scholar 

  24. Zhou, K.L., Chen, Z.Y., Guo, Y., Liao, Q.: Performance improvement of unidimensional continuous-variable quantum key distribution using heralded hybrid linear amplifier. Phys. Lett. A 384, 126074 (2020)

    Article  MathSciNet  Google Scholar 

  25. Opatrný, T., Kurizki, G., Welsch, D.G.: Improvement on teleportation of continuous variables by photon subtraction via conditional measurement. Phys. Rev. A 61, 032302 (2000)

    Article  ADS  Google Scholar 

  26. Kim, M.S., Park, E., Knight, P.L., Jeong, H.: Nonclassicality of a photon-subtracted Gaussian field. Phys. Rev. A 71, 043805 (2005)

    Article  ADS  Google Scholar 

  27. Kitagawa, A., Takeoka, M., Sasaki, M., Chefles, A.: Entanglement evaluation of non-Gaussian states generated by photon subtraction from squeezed states. Phys. Rev. A 73, 042310 (2006)

    Article  ADS  Google Scholar 

  28. Huang, P., He, G.Q., Fang, J., Zeng, G.H.: Performance improvement of continuous-variable quantum key distribution via photon subtraction. Phys. Rev. A 87, 012317 (2013)

    Article  ADS  Google Scholar 

  29. Yang, Y., Li, F.L.: Entanglement properties of non-Gaussian resources generated via photon subtraction and addition and continuous-variable quantum-teleportation improvement. Phys. Rev. A 80, 022315 (2009)

    Article  ADS  Google Scholar 

  30. Navarrete-Benlloch, C., García-Patrón, R., Shapiro, J.H., Cerf, N.J.: Enhancing quantum entanglement by photon addition and subtraction. Phys. Rev. A 86, 012328 (2012)

    Article  ADS  Google Scholar 

  31. Wang, K., Yu, X.T., Zhang, Z.C.: Two-qubit entangled state teleportation via optimal POVM and partially entangled GHZ state. Front. Phys. 13, 130320 (2018)

    Article  Google Scholar 

  32. Eisaman, M.D., Fan, J., Migdall, A., Polyakov, S.V.: Single-photon sources and detectors. Rev. Sci. Instrum. 87, 071101 (2011)

    Article  ADS  Google Scholar 

  33. Zhao, Y.J., Zhang, Y.C., Xu, B.J., Yu, S., Guo, H.: Continuous-variable measurement-device-independent quantum key distribution with virtual photon subtraction. Phys. Rev. A 97, 042328 (2018)

    Article  ADS  Google Scholar 

  34. Li, Z.Y., Zhang, Y.C., Wang, X.Y., Xu, B.J., Peng, X., Guo, H.: Non-gaussian postselection and virtual photon subtraction in continuous-variable quantum key distribution. Phys. Rev. A 93, 012310 (2016)

    Article  ADS  Google Scholar 

  35. Zhao, Y.J., Zhang, Y.C., Li, Z.Y., Yu, S., Guo, H.: Improvement of two-way continuous-variable quantum key distribution with virtual photon subtraction. Quantum Inf Process. 16, 184 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  36. Serafini, A., Paris, M.G.A., Illuminati, F., De Siena, S.: Quantifying decoherence in continuous variable systems. J. Opt. B:, Quantum Semiclass. Opt. 7, 4 (2005)

    Article  Google Scholar 

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 61872390).

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Authors and Affiliations

  1. School of Computer Science and Engineering, Central South University, Changsha, China

    Wei Zhao, Yanyan Feng, Xiaoxue Wang & Ronghua Shi

  2. School of Automation, Central South University, Changsha, 410083, China

    Xinchao Ruan & Ying Guo

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  1. Wei Zhao
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  2. Xinchao Ruan
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  3. Yanyan Feng
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Correspondence to Xinchao Ruan or Ronghua Shi.

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Appendix: : Calculation of the Symplectic Eigenvalues

Appendix: : Calculation of the Symplectic Eigenvalues

The symplectic eigenvalues λ3,4,5 of the matrix \( \gamma _{AHG}^{p_{B_{4}}}\) being the solutions of the third order polynomial

$$ t^{3}-{\varDelta_{1}^{3}} t^{2} -{\varDelta_{2}^{3}} t-{\varDelta_{3}^{3}}=0, $$
(30)

with the notation

$$ \begin{array}{@{}rcl@{}} {{\varDelta}_{1}^{3}}&=&{\lambda_{3}^{2}}+{\lambda_{4}^{2}}+{\lambda_{5}^{2}} \\ &=&{\det}{\gamma}_{A}+{\det}{\gamma}_{H}+{\det}{\gamma}_{G}\\ &&+2{\det} C_{A-H}+2{\det}C_{A-G}+2{\det} C_{H-G} ,\\ {{\varDelta}_{2}^{3}}&=&{\lambda_{3}^{2}} {\lambda_{4}^{2}} +{\lambda_{4}^{2}} {\lambda_{5}^{2}}+{\lambda_{3}^{2}} {\lambda_{5}^{2}} \\ &=&{\det}\gamma_{AH}+{\det}\gamma_{HG}+{\det}\gamma_{AG} \\ &=&2{\det}C_{AH-HG}+2{\det}C_{AH-AG}+2{\det}C_{HG-AH} , \\ {{\varDelta}_{3}^{3}}&=&{\lambda_{3}^{2}} {\lambda_{4}^{2}} {\lambda_{5}^{2}}={\det}\gamma_{AHG} , \end{array} $$
(31)

where

$$ \gamma_{AHG}^{p_{B_{4}}}= \left( \begin{array}{ccc} \gamma_{A} &C_{A-H} &C_{A-G} \\ C_{A-H}^{\mathrm{T}} &\gamma_{H} &C_{H-G} \\ C_{A-G}^{\mathrm{T}} &C_{H-G}^{\mathrm{T}} & \gamma_{G} \end{array} \right). $$
(32)

Besides, the matrix Cij−kl reads

$$ C_{ij-kl}= \left( \begin{array}{cc} \alpha_{ik} &\alpha_{il} \\ \alpha_{jk} &\alpha_{jl} \\ \end{array} \right), $$
(33)

where αmn is the elementary submatrice describing the correlations between a part of modes of the covariance matrice \(\gamma _{AHG}^{p_{B}}\).

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Zhao, W., Ruan, X., Feng, Y. et al. Enhancing the Unidimensional Continuous-Variable Quantum Key Distribution with Virtual Photon Subtraction. Int J Theor Phys 59, 2939–2950 (2020). https://doi.org/10.1007/s10773-020-04553-7

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