Non-coherent attack on the ping-pong protocol with completely entangled pairs of qutrits

Abstract

The non-coherent attack on the ping-pong protocol with completely entangled pairs of three-dimensional quantum systems (qutrits) is analyzed. The expression for the amount of the eavesdropper’s information as functions of attack detection probability is derived. It is shown that the security of the ping-pong protocol with pairs of qutrits is higher than the security of the protocol with pairs of qubits. It is also shown that with the use by legitimate users in a control mode of two mutually unbiased measuring bases, the ping-pong protocol with pairs of qutrits possesses only asymptotic security, as well as the protocol with entangled qubits.

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References

  1. 1

    Boström K., Felbinger T.: Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89(18), 187902 (2002)

    ADS  PubMed  Article  CAS  Google Scholar 

  2. 2

    Boström K., Felbinger T.: On the security of the ping-pong protocol. Phys. Lett. A 372(22), 3953–3956 (2008)

    MathSciNet  ADS  Article  MATH  CAS  Google Scholar 

  3. 3

    Cai Q.Y.: The “ping-pong” protocol can be attacked without eavesdropping. Phys. Rev. Lett. 91(10), 109801 (2003)

    ADS  PubMed  Article  CAS  Google Scholar 

  4. 4

    Cai Q.Y., Li B.W.: Improving the capacity of the Boström-Felbinger protocol. Phys. Rev. A 69(5), 054301 (2004)

    ADS  Article  CAS  Google Scholar 

  5. 5

    Cai Q.Y., Li B.W.: Deterministic secure communication without using entanglement. Chin. Phys. Lett. 21(4), 601–603 (2004)

    ADS  Article  Google Scholar 

  6. 6

    Chamoli A., Bhandari C.M.: Secure direct communication based on ping-pong protocol. Quantum Inf. Process. 8(4), 347–356 (2009)

    MathSciNet  MATH  Article  Google 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(4), 042317 (2003)

    ADS  Article  CAS  Google Scholar 

  8. 8

    Deng F.G., Long G.L.: Bidirectional quantum key distribution protocol with practical faint laser pulses. Phys. Rev. A 70(1), 012311 (2004)

    ADS  Article  CAS  Google Scholar 

  9. 9

    Deng F.G., Long G.L.: Secure direct communication with a quantum one-time pad. Phys. Rev. A 69(5), 052319 (2004)

    ADS  Article  CAS  Google Scholar 

  10. 10

    Gao T., Yan F.L., Wang Z.X.: Deterministic secure direct communication using GHZ–states and swapping quantum entanglement. J. Phys. A Math. Theor. 38(25), 5761–5770 (2005)

    MathSciNet  ADS  MATH  Article  Google Scholar 

  11. 11

    Joo J., Rudolph T., Sanders B.C.: A heralded two-qutrit entangled state. J. Phys. B At. Mol. Opt. Phys. 42(11), 114007 (2009)

    ADS  Article  CAS  Google Scholar 

  12. 12

    Lee H., Lim J., Yang H.: Quantum direct communication with authentication. Phys. Rev. A 73(4), 042305 (2006)

    ADS  Article  CAS  Google Scholar 

  13. 13

    Li X.H., Deng F.G., Li C.Y. et al.: Deterministic secure quantum communication without maximally entangled states. J. Korean Phys. Soc. 49(4), 1354–1359 (2006)

    MathSciNet  Google Scholar 

  14. 14

    Li X.H., Deng F.G., Zhou H.Y.: Improving the security of secure direct communication based on the secret transmitting order of particles. Phys. Rev. A 74(5), 054302 (2006)

    ADS  Article  CAS  Google Scholar 

  15. 15

    Li X.H., Li C.Y., Deng F.G. et al.: Quantum secure direct communication with quantum encryption based on pure entangled states. Chin. Phys. 16(8), 2149–2153 (2007)

    ADS  Article  MathSciNet  Google Scholar 

  16. 16

    Lin S., Wen Q.Y., Gao F., Zhu F.C.: Quantum secure direct communication with chi-type entangled states. Phys. Rev. A 78(6), 064304 (2008)

    ADS  Article  CAS  Google Scholar 

  17. 17

    Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    Google Scholar 

  18. 18

    Stinespring, W.F.: Positive functions on C*-algebras. In: Proceedings of the American Mathematical Society, vol. 6, pp. 211–216 (1955)

  19. 19

    Thew R., Acin A., Zbinden H., Gisin N.: Experimental realization of entangled qutrits for quantum communication. Quantum Inf. Comput. 4(2), 093–101 (2004)

    MathSciNet  Google Scholar 

  20. 20

    Vasiliu, E.V., Vasiliu, L.N.: Ping-pong protocol with three- and four-qubit Greenberger–Horne–Zeilinger states. Work. Odessa Polytech. Univ. 1(29), 171–176 (2008) (in Russian) http://nbuv.gov.ua/portal/natural/Popu/2008_1/3-4.pdf

  21. 21

    Vasiliu, E.V.: Asymptotic security of the ping-pong quantum direct communication protocol with three-qubit Greenberger–Horne–Zeilinger states. Georgian Elec. Sci. J. Comput. Sci. Telecomm. 3, 3–15 (2009) (in Russian) http://gesj.internet-academy.org.ge/gesj_articles/1427.pdf

    Google Scholar 

  22. 22

    Vasiliu, E.V., Nikolaenko, S.V.: Synthesis of the secure system of direct messages transfer based on the ping-pong protocol of quantum communication. Sci. Work. Odessa Natl. Acad. Telecomm. 1, 83–91 (2009) (in Russian) http://sbornik.onat.edu.ua/?art=338

    Google Scholar 

  23. 23

    Vaziri A., Pan J., Jennewein T., Weihs G., Zeilinger A.: Concentration of higher dimensional entanglement: Qutrits of photon orbital angular momentum. Phys. Rev. Lett. 91(22), 227902 (2003)

    ADS  PubMed  Article  CAS  Google Scholar 

  24. 24

    Wang Ch, Deng F.G., Long G.L.: Multi-step quantum secure direct communication using multi-particle Greenberger–Horne–Zeilinger state. Opt. Communic. 253(1), 15–20 (2005)

    ADS  Article  CAS  Google Scholar 

  25. 25

    Wang Ch, Deng F.G., Li Y.S., Liu X.S., Long G.L.: Quantum secure direct communication with high dimension quantum superdense coding. Phys. Rev. A 71(4), 044305 (2005)

    ADS  Article  CAS  Google Scholar 

  26. 26

    Wang J., Zhang Q., Tang C.J.: Multiparty controlled quantum secure direct communication using Greenberger–Horne–Zeilinger state. Opt. Communic. 266(2), 732–737 (2006)

    MathSciNet  ADS  Article  CAS  Google Scholar 

  27. 27

    Yan F.L., Zhang X.Q.: A scheme for secure direct communication using EPR pairs and teleportation. Eur. Phys. J. B 41(1), 75–78 (2004)

    ADS  Article  CAS  Google Scholar 

  28. 28

    Yen C.A., Horng S.J., Goan H.S. et al.: Quantum direct communication with mutual authentication. Quantum Inf. Comput. 9(5–6), 0376–0394 (2009)

    MathSciNet  Google Scholar 

  29. 29

    Zhang Zh J., Li Y., Man Zh X.: Improved Wojcik’s eavesdropping attack on ping-pong protocol without eavesdropping-induced channel loss. Phys. Lett. A 341(5–6), 385–389 (2005)

    ADS  Article  CAS  Google Scholar 

  30. 30

    Zhu A.D., Xia Y., Fan Q.B., Zhang S.: Secure direct communication based on secret transmitting order of particles. Phys. Rev. A 73(2), 022338 (2006)

    ADS  Article  CAS  Google Scholar 

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Correspondence to Eugene V. Vasiliu.

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Vasiliu, E.V. Non-coherent attack on the ping-pong protocol with completely entangled pairs of qutrits. Quantum Inf Process 10, 189–202 (2011). https://doi.org/10.1007/s11128-010-0188-8

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Keywords

  • Ping-pong protocol
  • Non-coherent attack
  • Eavesdropper’s amount of information
  • Asymptotic security