Quantum dialogue protocol with continuous-variable single-mode squeezed states

  • Ming-Hui ZhangEmail author
  • Zheng-Wen Cao
  • Chen He
  • Mei Qi
  • Jin-Ye Peng


Most of the information carriers applied in the existing quantum dialogue protocols are discrete-variable quantum states. However, there are certain restrictions on the generation and detection of discrete-variable quantum states with current techniques. Continuous-variable quantum dialogue can overcome these limitations and has advantages of simple preparation, easy detection and implementation and high channel capacity. Such properties are strong improvements with respect to discrete-variable quantum dialogue. In this paper, we propose a continuous-variable quantum dialogue protocol with single-mode squeezed states. Both users in the protocol can encode their own two bits of information into optical modes with translation operations by using the phase space of a bosonic mode. The protocol improves the channel capacity as each travelling mode carries two bits of information. The security of the protocol is guaranteed by the randomly selected decoy states and encoding time slot. The protocol has been proved to be secure against information leakage problem and some common attacks.


Quantum dialogue Continuous variable Single-mode squeezed states 



This work is supported by the National Natural Science Foundation of China (Grant No. 61801385) and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2018JM6123).


  1. 1.
    Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: Proceedings of the IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India. pp. 175–179 (1984)Google Scholar
  2. 2.
    Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121–3124 (1992)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    Ekert, A.K.: Quantum cryptography based on bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without bell theorem. Phys. Rev. Lett. 68, 557–559 (1992)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Deng, F.G., Long, G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    Lo, H.K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012)ADSCrossRefGoogle Scholar
  7. 7.
    Deng, F.G., Long, G.L., Liu, X.S.: Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block. Phys. Rev. A 68, 042317 (2003)ADSCrossRefGoogle Scholar
  8. 8.
    Zhang, W., Ding, D.S., Sheng, Y.B., et al.: Quantum secure direct communication with quantum memory. Phys. Rev. Lett. 118, 220501 (2017)ADSCrossRefGoogle Scholar
  9. 9.
    Deng, F.G., Long, G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69, 052319 (2004)ADSCrossRefGoogle Scholar
  10. 10.
    Hu, J.Y., Yu, B., Jing, M.Y., et al.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5, e16144 (2016)CrossRefGoogle Scholar
  11. 11.
    Wang, J., Zhang, Q., Tang, C.J.: Quantum secure direct communication based on order rearrangement of single photons. Phys. Lett. A 358, 256–258 (2006)ADSCrossRefGoogle Scholar
  12. 12.
    Zhu, F., Zhang, W., Sheng, Y.B., Huang, Y.D.: Experimental long-distance quantum secure direct communication. Sci. Bull. 62, 1519–1524 (2017)CrossRefGoogle Scholar
  13. 13.
    Wang, C., Deng, F.G., Li, Y.S., et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    Cai, Q.Y., Li, B.W.: Deterministic secure communication without using entanglement. Chin. Phys. Lett. 21, 601–603 (2004)ADSCrossRefGoogle Scholar
  15. 15.
    Li, X.H., Deng, F.G., Li, C.Y., et al.: Deterministic secure quantum communication without maximally entangled states. J. Korean Phys. Soc. 49, 1354–1359 (2006)Google Scholar
  16. 16.
    Bostrom, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    Ji, X., Zhang, S.: Secure quantum dialogue based on single-photon. Chin. Phys. 15, 1418–1420 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Shi, G.F., Xi, X.Q., Hu, M.L., Yue, R.H.: Quantum dialogue by using single photons. Opt. Commun. 283, 1984–1986 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    Naseri, M.: An efficient protocol for quantum secure dialogue with authentication by using single photons. Int. J. Quantum Inf. 9, 1677–1684 (2011)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Luo, Y.P., Lin, C.Y., Hwang, T.: Efficient quantum dialogue using single photons. Quantum Inf. Process. 13, 2451–2461 (2014)ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    Nguyen, B.A.: Quantum dialogue. Phys. Lett. A 328, 6–10 (2004)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Zheng, C., Long, G.F.: Quantum secure direct dialogue using Einstein–Podolsky–Rosen pairs. Sci. China Phys. Mech. Astron. 57, 1238–1243 (2014)ADSCrossRefGoogle Scholar
  23. 23.
    Man, Z.X., Xia, Y.J.: Controlled bidirectional quantum direct communication by using a GHZ state. Chin. Phys. Lett. 23, 1680–1682 (2006)ADSCrossRefGoogle Scholar
  24. 24.
    Xia, Y., Song, J., Nie, J., Song, H.S.: Controlled secure quantum dialogue using a pure entangled GHZ states. Commun. Theor. Phys. 48, 841–846 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Kao, S.H., Hwang, T.: Controlled quantum dialogue using cluster states. Quantum Inf. Process. 16, UNSP 139 (2017)Google Scholar
  26. 26.
    Li, Y.H., Li, X.L., Sang, M.H.: Bidirectional controlled quantum teleportation and secure direct communication using five-qubit entangled state. Quantum Inf. Process. 12, 3835–3844 (2017)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Gao, F., Guo, F.Z., Wen, Q.Y., Zhu, F.C.: Revisiting the security of quantum dialogue and bidirectional quantum secure direct communication. Sci. China Ser. G Phys. Mech. Astron. 51, 559–566 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Wang, H., Zhang, Y.Q., Liu, X.F., Hu, Y.P.: Efficient quantum dialogue using entangled states and entanglement swapping without information leakage. Quantum Inf. Process. 15, 2593–2603 (2016)ADSMathSciNetCrossRefGoogle Scholar
  29. 29.
    Gao, G.: Two quantum dialogue protocols without information leakage. Opt. Commun. 283, 2288–2293 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    Ye, T.Y.: Quantum dialogue without information leakage using a single quantum entangled state. Int. J. Theor. Phys. 53, 3719–3727 (2014)CrossRefGoogle Scholar
  31. 31.
    Hwang, T., Luo, Y.P.: Probabilistic authenticated quantum dialogue. Quantum Inf. Process. 14, 4631–4650 (2015)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    Wang, X.B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005)ADSCrossRefGoogle Scholar
  33. 33.
    Scarani, V., Acin, A., Ribordy, G., Gisin, N.: Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulse implementations. Phys. Rev. Lett. 92, 057901 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    Grosshans, F., Grangier, P.: Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    Grosshans, F., Van Assche, G., Wenger, J.: Quantum key distribution using gaussian-modulated coherent states. Nature 421, 238–241 (2003)ADSCrossRefGoogle Scholar
  36. 36.
    Silberhorn, C., Ralph, T.C., Lutkenhaus, N.: Continuous variable quantum cryptography: beating the 3 dB loss limit. Phys. Rev. Lett. 89, 167901 (2002)ADSCrossRefGoogle Scholar
  37. 37.
    Garcia-Patron, R., Cerf, N.J.: Unconditional optimality of Gaussian attacks against continuous-variable quantum key distribution. Phys. Rev. Lett. 97, 190503 (2006)ADSCrossRefGoogle Scholar
  38. 38.
    Wang, X.B., Hiroshima, T., Tomita, A.: Quantum information with Gaussian states. Phys. Rep. Rev. Sect. Phys. Lett. 448, 1–111 (2007)MathSciNetGoogle Scholar
  39. 39.
    Lodewyck, J., Bloch, M., Garcia-Patron, R.: Quantum key distribution over 25 km with an all-fiber continuous-variable system. Phys. Rev. A 76, 042305 (2007)ADSCrossRefGoogle Scholar
  40. 40.
    Jouguet, P., Kunz-Jacques, S., Leverrier, A.: Long-distance continuous-variable quantum key distribution with a Gaussian modulation. Phys. Rev. A 84, 062317 (2011)ADSCrossRefGoogle Scholar
  41. 41.
    Madsen, L.S., Usenko, V.C., Lassen, M.: Continuous variable quantum key distribution with modulated entangled states. Nat. Commun. 3, 1083 (2012)CrossRefGoogle Scholar
  42. 42.
    Weedbrook, C., Pirandola, S., Ralph, T.C.: Continuous-variable quantum key distribution using thermal states. Phys. Rev. A 86, 022318 (2012)ADSCrossRefGoogle Scholar
  43. 43.
    Furrer, F., Franz, T., Berta, M.: Continuous variable quantum key distribution: finite-key analysis of composable security against coherent attacks. Phys. Rev. Lett. 109, 100502 (2012)ADSCrossRefGoogle Scholar
  44. 44.
    Jouguet, P., Kunz-Jacques, S., Leverrier, A.: Experimental demonstration of long-distance continuous-variable quantum key distribution. Nat. Photonics 7, 378–381 (2013)ADSCrossRefGoogle Scholar
  45. 45.
    Pirandola, S., Ottaviani, C., Spedalieri, G.: High-rate measurement-device-independent quantum cryptography. Nat. Photon. 9, 397–402 (2015)ADSCrossRefGoogle Scholar
  46. 46.
    Guo, Y., Liao, Q., Wang, Y.J.: Performance improvement of continuous-variable quantum key distribution with an entangled source in the middle via photon subtraction. Phys. Rev. A 95, 032304 (2017)ADSCrossRefGoogle Scholar
  47. 47.
    He, G.Q., Zhu, J., Zeng, G.H.: Quantum secure communication using continuous variable Einstein–Podolsky–Rosen correlations. Phys. Rev. A 73, 012314 (2006)ADSCrossRefGoogle Scholar
  48. 48.
    Pirandola, S., Braunstein, S.L., Mancini, S.: Quantum direct communication with continuous variables. EPL 84, 20013 (2008)ADSCrossRefGoogle Scholar
  49. 49.
    Meslouhi, A., Hassouni, Y.: A quantum secure direct communication protocol using entangled modified spin coherent states. Quantum Inf. Process. 12, 2603–2621 (2013)ADSCrossRefGoogle Scholar
  50. 50.
    Li, Y., Ji, C.L., Ji, S.R., Xu, M.T.: Continuous variable quantum secure direct communication in non-markovian channel. Int. J. Theor. Phys. 54, 1968–1973 (2015)MathSciNetCrossRefGoogle Scholar
  51. 51.
    Guerra, A.G.D.A.H., Rios, F.F.S., Ramos, R.V.: Quantum secure direct communication of digital and analog signals using continuum coherent states. Quantum Inf. Process. 15, 4747–4758 (2016)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Yu, Z.B., Gong, L.H., Zhu, Q.B., et al.: Efficient three-party quantum dialogue protocol based on the continuous variable GHZ states. Int. J. Theor. Phys. 55, 3147–3155 (2016)MathSciNetCrossRefGoogle Scholar
  53. 53.
    Yu, Z.B., Gong, L.H., Wen, R.H.: Novel multiparty controlled bidirectional quantum secure direct communication based on continuous-variable states. Int. J. Theor. Phys. 55, 1447–1459 (2016)CrossRefGoogle Scholar
  54. 54.
    Zhou, N.R., Li, J.F., Yu, Z.B., et al.: New quantum dialogue protocol based on continuous-variable two-mode squeezed vacuum states. Quantum Inf. Process. 11, UNSP 4 (2017)Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Information Science and TechnologyNorthwest UniversityXi’anChina

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