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Continuous variable direct secure quantum communication using Gaussian states

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Abstract

Continuous variable one-way and controlled two-way direct secure quantum communication schemes have been designed using Gaussian states. Specifically, a scheme for continuous variable quantum secure direct communication and another scheme for continuous variable controlled quantum dialogue are proposed using single-mode squeezed coherent states. The security of the proposed schemes against a set of attacks (e.g., Gaussian quantum cloning machine and intercept–resend attacks) has been proved. Further, it is established that the proposed schemes do not require two-mode squeezed states, which are essential for a set of existing proposals. The controlled two-way communication scheme is shown to be very general in nature as it can be reduced to schemes for various relatively simpler cryptographic tasks such as controlled deterministic secure communication, quantum dialogue, and quantum key distribution. In addition, it is briefly discussed that the proposed schemes can provide us tools to design quantum cryptographic solutions for several socioeconomic problems.

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References

  1. Dowling, J.P., Milburn, G.J.: Quantum technology: the second quantum revolution. Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 361, 1655–1674 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  2. Bennett, C.H., Brassard, G.: Quantum cryptography: public key distribution and coin tossing. In: International Conference on Computer System and Signal Processing, pp. 175–179. IEEE (1984)

  3. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  MATH  Google Scholar 

  4. Pathak, A.: Elements of Quantum Computation and Quantum Communication. Taylor & Francis, New York (2013)

    Book  MATH  Google Scholar 

  5. Shenoy-Hejamadi, A., Pathak, A., Radhakrishna, S.: Quantum cryptography: key distribution and beyond. Quanta 6, 1–47 (2017)

    Article  MathSciNet  Google Scholar 

  6. Boström, K., Felbinger, T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002)

    Article  ADS  Google Scholar 

  7. Deng, F.-G., Long, G.-L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  8. Hu, J., Yu, B., Jing, M.: Experimental quantum secure direct communication with single photons. Light Sci. Appl. 5, e16144 (2016)

    Article  Google Scholar 

  9. Long, G.-L., Deng, F.-G., Wang, C., et al.: Quantum secure direct communication and deterministic secure quantum communication. Front. Phys. China 2, 251–272 (2007)

    Article  ADS  Google Scholar 

  10. Nguyen, B.A.: Quantum dialogue. Phys. Lett. A 328, 6–10 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Thapliyal, K., Pathak, A.: Applications of quantum cryptographic switch: various tasks related to controlled quantum communication can be performed using Bell states and permutation of particles. Quantum Inf. Process. 14, 2599–2616 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Andersen, U.L., Leuchs, G., Silberhorn, C.: Continuous-variable quantum information processing. Laser Photonics Rev. 4, 337–354 (2010)

    Article  ADS  Google Scholar 

  14. Weedbrook, C., Pirandola, S., García-Patrón, R., et al.: Gaussian quantum information. Rev. Mod. Phys. 84, 621 (2012)

    Article  ADS  Google Scholar 

  15. Hillery, M.: Quantum cryptography with squeezed states. Phys. Rev. A 61, 022309 (2000)

    Article  ADS  Google Scholar 

  16. Gottesman, D., Preskill, J.: Secure quantum key distribution using squeezed states. Phys. Rev. A 63, 022309 (2001)

    Article  ADS  Google Scholar 

  17. Reid, M.D.: Quantum cryptography with a predetermined key, using continuous-variable Einstein–Podolsky–Rosen correlations. Phys. Rev. A 62, 062308 (2000)

    Article  ADS  Google Scholar 

  18. Ralph, T.C.: Continuous variable quantum cryptography. Phys. Rev. A 61, 010303 (1999)

    Article  MathSciNet  Google Scholar 

  19. Ralph, T.C.: Security of continuous-variable quantum cryptography. Phys. Rev. A 62, 062306 (2000)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Srikara, S., Thapliyal, K., Pathak, A.: Continuous variable B92 quantum key distribution protocol using single photon added and subtracted coherent states (2019). arXiv preprint arXiv:1906.07768

  22. Pirandola, S., Mancini, S., Lloyd, S., Braunstein, S.L.: Continuous-variable quantum cryptography using two-way quantum communication. Nat. Phys. 4, 726 (2008)

    Article  Google Scholar 

  23. Yuan, L., Chunlei, J., Shunru, J., Mantao, X.: Continuous variable quantum secure direct communication in non-Markovian channel. Int. J. Theor. Phys. 54, 1968–1973 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Marino, A.M., Stroud Jr., C.: Deterministic secure communications using two-mode squeezed states. Phys. Rev. A 74, 022315 (2006)

    Article  ADS  Google Scholar 

  25. Zhou, N.-R., Li, J.-F., Yu, Z.-B., Gong, L.-H., Farouk, A.: New quantum dialogue protocol based on continuous-variable two-mode squeezed vacuum states. Quantum Inf. Process. 16, 4 (2017)

    Article  ADS  MATH  Google Scholar 

  26. Zhang, M.-H., Cao, Z.-W., He, C., Qi, M., Peng, J.-Y.: Quantum dialogue protocol with continuous-variable single-mode squeezed states. Quantum Inf. Process. 18, 83 (2019)

    Article  ADS  MATH  Google Scholar 

  27. Yu, Z.-B., Gong, L.-H., Zhu, Q.-B., Cheng, S., Zhou, N.-R.: Efficient three-party quantum dialogue protocol based on the continuous variable GHZ states. Int. J. Theor. Phys. 55, 3147–3155 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Gong, L.-H., Tian, C., Li, J.-F., Zou, X.: Quantum network dialogue protocol based on continuous-variable GHZ states. Quantum Inf. Process. 17, 331 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. Saxena, A., Thapliyal, K., Pathak, A.: Continuous variable controlled quantum dialogue and secure multiparty quantum computation (2019). arXiv preprint arXiv:1902.00458

  30. Thapliyal, K., Sharma, R.D., Pathak, A.: Protocols for quantum binary voting. Int. J. Quantum Inf. 15, 1750007 (2017)

    Article  MATH  Google Scholar 

  31. Shukla, C., Thapliyal, K., Pathak, A.: Semi-quantum communication: protocols for key agreement, controlled secure direct communication and dialogue. Quantum Inf. Process. 16, 295 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Sharma, R.D., Thapliyal, K., Pathak, A.: Quantum sealed-bid auction using a modified scheme for multiparty circular quantum key agreement. Quantum Inf. Process. 16, 169 (2017)

    Article  ADS  MATH  Google Scholar 

  33. Thapliyal, K., Sharma, R.D., Pathak, A.: Orthogonal-state-based and semi-quantum protocols for quantum private comparison in noisy environment. Int. J. Quantum Inf. 16, 1850047 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  34. Thapliyal, K., Pathak, A.: Quantum e-commerce: a comparative study of possible protocols for online shopping and other tasks related to e-commerce. Quantum Inf. Process. 18, 191 (2019)

    Article  ADS  Google Scholar 

  35. Yao, A.C.: Protocols for secure computations. In: 23rd Annual Symposium on Foundations of Computer Science, 1982, SFCS’08, pp. 160–164. IEEE (1982)

  36. Villar, AdS, Cruz, L., Cassemiro, K.N., Martinelli, M., Nussenzveig, P.: Generation of bright two-color continuous variable entanglement. Phys. Rev. Lett. 95, 243603 (2005)

    Article  ADS  Google Scholar 

  37. Lassen, M., Leuchs, G., Andersen, U.L.: Continuous variable entanglement and squeezing of orbital angular momentum states. Phys. Rev. Lett. 102, 163602 (2009)

    Article  ADS  Google Scholar 

  38. Dos Santos, B.C., Dechoum, K., Khoury, A.: Continuous-variable hyperentanglement in a parametric oscillator with orbital angular momentum. Phys. Rev. Lett. 103, 230503 (2009)

    Article  Google Scholar 

  39. Liu, K., Guo, J., Cai, C., Guo, S., Gao, J.: Experimental generation of continuous-variable hyperentanglement in an optical parametric oscillator. Phys. Rev. Lett. 113, 170501 (2014)

    Article  ADS  Google Scholar 

  40. Thapliyal, K., Pathak, A., Sen, B., Peřina, J.: Higher-order nonclassicalities in a codirectional nonlinear optical coupler: quantum entanglement, squeezing, and antibunching. Phys. Rev. A 90, 013808 (2014)

    Article  ADS  Google Scholar 

  41. Thapliyal, K., Pathak, A., Sen, B., Perina, J.: Nonclassical properties of a contradirectional nonlinear optical coupler. Phys. Lett. A 378, 3431–3440 (2014)

    Article  ADS  MATH  Google Scholar 

  42. Thapliyal, K., Samantray, N.L., Banerji, J., Pathak, A.: Comparison of lower- and higher-order nonclassicality in photon added and subtracted squeezed coherent states. Phys. Lett. A 381, 3178–3187 (2017)

    Article  Google Scholar 

  43. Agarwal, G.S.: Quantum Optics. Cambridge University Press, Cambridge (2013)

    MATH  Google Scholar 

  44. Wigner, E.P.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749 (1932)

    Article  ADS  MATH  Google Scholar 

  45. Strawberry fields interactive. https://strawberryfields.ai.Xanadu. Accessed on 10 Dec (2018)

  46. Thapliyal, K., Banerjee, S., Pathak, A., Omkar, S., Ravishankar, V.: Quasiprobability distributions in open quantum systems: spin-qubit systems. Ann. Phys. 362, 261–286 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  47. Thapliyal, K., Banerjee, S., Pathak, A.: Tomograms for open quantum systems: in (finite) dimensional optical and spin systems. Ann. Phys. 366, 148–167 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  48. Thapliyal, K., Pathak, A., Banerjee, S.: Quantum cryptography over non-Markovian channels. Quantum Inf. Process. 16, 115 (2017)

    Article  ADS  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

AP acknowledges the support from Interdisciplinary Cyber Physical Systems (ICPS) programme of the Department of Science and Technology (DST), India, Grant No.: DST/ICPS/QuST/Theme-1/2019/14. KT acknowledges the financial support from the Operational Programme Research, Development and Education—European Regional Development Fund Project No. CZ.02.1.01/0.0/0.0/16_019/0000754 of the Ministry of Education, Youth and Sports of the Czech Republic.

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Authors and Affiliations

  1. Indian Institute of Science Education and Research, Pune, India

    S. Srikara

  2. RCPTM, Joint Laboratory of Optics of Palacky University and Institute of Physics of Academy of Science of the Czech Republic, Faculty of Science, Palacky University, 17. listopadu 12, 771 46, Olomouc, Czech Republic

    Kishore Thapliyal

  3. Jaypee Institute of Information Technology, A-10, Sector-62, Noida, UP, 201309, India

    Anirban Pathak

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  1. S. Srikara
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Srikara, S., Thapliyal, K. & Pathak, A. Continuous variable direct secure quantum communication using Gaussian states. Quantum Inf Process 19, 132 (2020). https://doi.org/10.1007/s11128-020-02627-3

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