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An Efficient Scheme of Quantum Wireless Multi-hop Communication using Coefficient Matrix

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Abstract

By defining the coefficient matrix, a new quantum teleportation scheme in quantum wireless multi-hop network is proposed. With the help of intermediate nodes, an unknown qubit state can be teleported between two distant nodes which do not share entanglement in advance. Arbitrary Bell pairs and entanglement swapping are utilized for establishing quantum channel among intermediate nodes. Using collapsed matrix, the initial quantum state can be perfectly recovered at the destination.

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References

  1. Bloch, M., Rodrigues, M.R.D., McLaughlin, S.W., Barros, J.: Wireless information-theoretic security. IEEE Trans. Inf. Theory 54, 2515 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Kannhavong, B., Nakayama, H., Nemoto, Y., Kato, N., Jamalipour, A.: A survey of routing attacks in mobile ad hoc networks. IEEE Wiresss Comm. 14, 85 (2007)

    Article  Google Scholar 

  3. Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev.Lett. 70, 1895–1899 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, M., Zeilinger, A.: Experimental quantum teleportation. Nature 390, 575–579 (1997)

    Article  ADS  Google Scholar 

  5. Boschi, D., Branca, S., Martini, F.D., Hardy, L., Popescu, S.: Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett 80, 1121 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Yang, C.P., Chu, S.I., Han, S.: Efficient many-party controlled teleportation of multiqubit quantum information via entanglement. Phys. Rev. A 70, 022329 (2004)

    Article  ADS  Google Scholar 

  7. Barrett, M.D., Chiaverini, J., Schaetz, T., et al.: Deterministic quantum teleportation of atomic qubits. Nature 429, 737–739 (2004)

    Article  ADS  Google Scholar 

  8. Zhang, Z.J.: Controlled teleportation of an arbitrary n-qubit quantum information using quantum secret sharing of classical message. Phys. Lett. A 352, 55–58 (2006)

    Article  ADS  MATH  Google Scholar 

  9. Deng, F.G., Li, C.Y., Li, Y.S., Zhou, H.Y., Wang, Y.: Symmetric multiparty-controlled teleportation of an arbitrary two-particle entanglement. Phys. Rev. A 72, 022338 (2005)

    Article  ADS  Google Scholar 

  10. Gao, T., Yan, F.L., Wang, Z.X.: Controlled quantum teleportation and secure direct communication. Chinese Phys. 14, 893 (2005)

    Article  ADS  Google Scholar 

  11. Zha, X.W., Zou, Z.C., Qi, J.X., Song, H.Y.: Bidirectional Quantum Controlled Teleportation via Five-Qubit Cluster State. Int. J. Theor.Phys. 52, 1740–1744 (2012)

    Article  MathSciNet  Google Scholar 

  12. Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India, p 175. IEEE Press, New York (1984)

  13. Ekert, A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661–663 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Bennett, C.H., Brassard, G., Mermin, N.D.: Quantum cryptography without Bell’s theorem. Phys. Rev. Lett. 68, 557–559 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Hwang, W.Y.: Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003)

    Article  ADS  Google Scholar 

  18. Wang, X.B.: Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005)

    Article  ADS  Google Scholar 

  19. Lo, H.K., Ma, X.F., Chen, K.: Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005)

    Article  ADS  Google Scholar 

  20. Li, X.H., Deng, F.G., Zhou, H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)

    Article  ADS  Google Scholar 

  21. Hillery, M., Buzek, V., Berthiaume, A: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  22. Cleve, R., Gottesman, D., Lo, H.K.: How to Share a Quantum Secret. Phys. Rev. Lett. 83, 648–651 (1999)

    Article  ADS  Google Scholar 

  23. Lance, A.M., Symul, T., Bowen, W.P., Sanders, B.C., Lam, P.K.: Tripartite Quantum State Sharing. Phys. Rev. Lett. 92, 177903 (2004)

    Article  ADS  Google Scholar 

  24. Deng, F.G., Li, X.H., Li, C.Y., Zhou, P., Zhou, H.Y.: Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs. Phys. Rev. A 72, 044301 (2005)

    Article  ADS  Google Scholar 

  25. Gordon G., Rigolin, G.: Generalized quantum-state sharing. Phys. Rev. A 73, 062316 (2006)

    Article  ADS  Google Scholar 

  26. Gaertner, S., Kurtsiefer, C., Bourennane, M., Weinfurter, H.: Experimental demonstration of four-party quantum secret sharing. Phys. Rev. Lett. 98, 020503 (2007)

    Article  ADS  Google Scholar 

  27. Schmid, C., Trojek, P., Bourennane, M., Kurtsiefer, C., Zukowski, M., Weinfurter, H.: Experimental Single Qubit Quantum Secret Sharing. Phys. Rev. Lett 95, 230505 (2005)

    Article  ADS  MATH  Google Scholar 

  28. Zhou, N.Y., Song, H.C., Gong, L.H.: Continuous Variable Quantum Secret Sharing via Quantum Teleportation. Int. J. Theor.Phys. 52, 4174–4184 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  29. Long, G.L., Liu, X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  30. Wang, C., et al.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)

    Article  ADS  Google Scholar 

  31. 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)

    Article  ADS  Google Scholar 

  32. Wang, C., et al.: Multi-step quantum secure direct communication using multi-particle Green-Horne-Zeilinger state. Opt. Commun. 253, 15–20 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  35. Wang, T.J., Li, T., Du, F.F., Deng, F.G.: High-capacity quantum secure direct communication based on quantum hyperdense coding with hyperentanglement. Chin. Phys. Lett. 28, 040305 (2011)

    Article  ADS  Google Scholar 

  36. Gu, B., et al.: Robust quantum secure direct communication with a quantum one-time pad over a collective-noise channel. Sci. China:Phys. Mech. Astron. 54, 942–947 (2011)

    ADS  Google Scholar 

  37. Shi, J., Gong, Y.X., Xu, P., Zhu, S.N., Zhan, Y.B.: Quantum Secure Direct Communication by Using Three-Dimensional Hyperentanglement. Commun. Theor. Phys. 56, 831 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. Wu, Y.H., Zhai, W.D., Cao, W.Z., Li, C.: Quantum Secure Direct Communication by Using General Entangled States. Int. J. Theor.Phys. 50, 325–331 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  39. Gao, G., Fang, M., Yang, R.M.: Quantum Secure Direct Communication by Swapping Entanglements of 33-Dimensional Bell States. Int. J. Theor. Phys. 50, 882–887 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  40. Liu, D., Chen, J.L., Jiang, W.: High-Capacity Quantum Secure Direct Communication with Single Photons in Both Polarization and Spatial-Mode Degrees of Freedom. Int. J. Theor. Phys. 51, 2923–2929 (2012)

    Article  MATH  Google Scholar 

  41. Sun, Z.W., Du, R.G., Long, D.Y.: Quantum Secure Direct Communication with Two-Photon Four-Qubit Cluster States. Int. J. Theor. Phys 51, 1946–1952 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  42. Ren, B.C., et al.: Photonic spatial Bell-state analysis for robust quantum secure direct communication using quantum dot-cavity systems. Eur. Phys. J. D 67, 30 (2013)

    Article  ADS  Google Scholar 

  43. Gu, B., et al.: Robust Quantum Secure Communication with Spatial Quantum States of Single Photons. Int. J. Theor. Phys 52, 4461–4469 (2013)

    Article  MATH  Google Scholar 

  44. Zhang, Q.N., Li, C.C., Li, Y.H., Nie, Y.Y.: Quantum Secure Direct Communication Based on Four-Qubit Cluster States. Int. J. Theor.Phys. 52, 22–27 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  45. Chang, Y., Xu, C.X., Zhang, S.B., Yan, L.L.: Quantum secure direct communication and authentication protocol with single photons. Chin. Sci. Bulletin 58, 4571–4576 (2013)

    Article  Google Scholar 

  46. Yan, F.L., Zhang, X.: A scheme for secure direct communication using EPR pairs and teleportation. Euro. Phys. J. B 41, 75 (2004)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. Man, Z.X., Zhang, Z.J., Li, Y.: Deterministic Secure Direct Communication by Using Swapping Quantum Entanglement and Local Unitary Operations. Chin. Phys. Lett. 22, 18 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  50. 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, 054302 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Wang, J., Zhang, Q., Tang, C.J.: Quantum secure direct communication based on order rearrangement of single photons. Phys. Lett. A 358, 256 (2006)

    Article  ADS  MATH  Google Scholar 

  53. Li, X.H., Deng, F.G., Li, C.Y., Liang, Y.J., Zhou, P., Zhou, H.Y.: Deterministic secure quantum communication without maximally entangled states. J. Korean Phys. Soc. 49, 1354 (2006)

    Google Scholar 

  54. Wang, J., Zhang, Q., Tang, C.J.: Quantum secure direct communication without a pre-established secure quantum channel. Int. J. Quantum Inform. 4, 925 (2006)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  56. Man, Z.X., Zhang, Z.J., Li, Y.: Quantum Dialogue Revisited. Chin. Phys. Lett. 22, 22 (2005)

    Article  ADS  Google Scholar 

  57. Ji, X., Zhang, S.: Secure quantum dialogue based on single-photon. Chin. Phys. 15(07), 1418–03 (2006)

    Article  ADS  Google Scholar 

  58. Agrawal, D.P., Zeng, Q.A.: Introduction to Wireless and Mobile Systems. CA: Brooks Cole, Pacific Grove (2002)

  59. Rappaport, T.S.: Wireless Communications Principles And Practice. NJ. Prentice-Hall, Englewood Cliffs (2001)

    Google Scholar 

  60. Cheng, S.T., Wang, C.Y., Tao, M.H.: Quantum communication for wireless wide-area networks. IEEE J. Sel. Area Comm. 23, 1424–1432 (2005)

    Article  Google Scholar 

  61. Bacinoglu, T., Gulbahar, B., Akan, O.B.: Constant fidelity entanglement flow in quantum communication networks. 2010 Proceedings of IEEE Global Telecommunications Conference, Miami USA, December 6-10, 1-5 (2010)

  62. Yu, X.T., Xu, J., Zhang, Z.C.: Routing protocol for wireless ad hoc quantum communication network based on quantum teleportation. Acta Phys. Sin. 61, 220303 (2012). in Chinese

    Google Scholar 

  63. Wang, K., Yu, X.T., Lu, S.L., Gong, Y.X.: Quantum wireless multihop communication based on arbitrary Bell pairs and teleportation. Phys. Rev. A 89, 022329 (2014)

    Article  ADS  Google Scholar 

  64. Zha, X.W., Qi, J.X., Song, H.Y.: Channel matrix, measurement matrix and collapsed matrix in teleportation. arXiv:1402.1240

  65. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2010)

    Book  MATH  Google Scholar 

  66. Sheng, Y. B., Zhou, L., Cheng, W.W., Gong, L.Y., Zhao, S.M., Zheng, B.Y.: Efficient entanglement purification in quantum repeaters. Chin. Phys. B 21, 030307 (2012)

    Article  ADS  Google Scholar 

  67. Yao, X.C., Wang, T.X., Xu, P., Lu, H., Pan, G.S., Bao, X.H., Peng, C.Z., Lu, C.Y., Chen, Y.A., Pan, J.W.: Observation of eight-photon entanglement. Natrue Photonics 6, 225–228 (2012)

    Article  ADS  Google Scholar 

  68. Perkins, C.E., Royer, E.M.: Ad-hoc on-demand distance vector routing. In: Proceedings of the Second IEEE Workshop on Mobile Computing Systems and Applications, pp 90–100 (1999)

  69. Pemberton-Ross, P.J., Kay, A.: Perfect quantum routing in regular spin networks. Phys. Rev. Lett. 106, 020503 (2011)

    Article  ADS  Google Scholar 

  70. Fowler, A.G., Wang, D.S., Hill, C.D., Ladd, T.D., Meter, R.V., Hollenberg, L.C.L.: Surface code quantum communication. Phys. Rev. Lett. 104, 180503 (2010)

    Article  ADS  Google Scholar 

  71. Meter, R.V., Satoh, T., Ladd, T.D., Munro, W.J., Nemoto, K.: Path selection for quantum repeater networks. Networking Sci. 3, 82–95 (2013)

    Article  Google Scholar 

  72. Bennett, C.H., Brassard, G., Popescu, S., Schumacher, B., Smolin, J.A., Wootters, W.K.: Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)

    Article  ADS  Google Scholar 

  73. Deutsch, D., Ekert, A., Jozsa, R., Macchiavello, C., Popescu, S., Sanpera, A.: Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996)

    Article  ADS  Google Scholar 

  74. Pan, J.W., Simon, C., Zellinger, A.: Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001)

    Article  ADS  Google Scholar 

  75. Simon, C., Pan, J.W.: Polarization entanglement purification using spatial entanglement. Phys. Rev. Lett. 89, 257901 (2002)

    Article  ADS  Google Scholar 

  76. Sheng, Y.B., Deng, F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)

    Article  ADS  Google Scholar 

  77. Li, X.H.: Deterministic polarization-entanglement purification using spatial entanglement. Phys. Rev. A 82, 044304 (2010)

    Article  ADS  Google Scholar 

  78. Deng, F.G.: Efficient multipartite entanglement purification with the entanglement link from a subspace. Phys. Rev. A 84, 052312 (2011)

    Article  ADS  Google Scholar 

  79. Ren, B.C., Deng, F.G.: Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities. Laser Phys. Lett. 10, 115201 (2013)

    Article  ADS  Google Scholar 

  80. Murao, M., Plenio, M.B., Popescu, S., Vedral, V., Knight, P. L.: Multiparticle entanglement purification protocols. Phys. Rev. A 57, R4075 (1998)

    Article  ADS  Google Scholar 

  81. Cheong, Y.W., Lee, S.W., Lee, J., Lee, H.W.: Entanglement purification for high-dimensional multipartite systems. Phys. Rev. A 76, 042314 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  82. Bennett, C.H., Bernstein, H.J., Popescu, S., Schumacher, B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046–2052 (1996)

    Article  ADS  Google Scholar 

  83. Yamamoto, T., Koashi, M., Imoto, N.: Concentration and purification scheme for two partially entangled photon pairs. Phys. Rev. A 64, 012304 (2001)

    Article  ADS  Google Scholar 

  84. Zhao, Z., Pan, J.W., Zhan, M.S.: Practical scheme for entanglement concentration. Phys. Rev. A 64, 014301 (2001)

    Article  ADS  Google Scholar 

  85. Sheng, Y.B., Deng, F.G., Zhou, H.Y.: Single-photon entanglement concentration for long-distance quantum communication. Quantum Inf. Comput. 10, 0272–0281 (2010)

    MathSciNet  Google Scholar 

  86. Deng, F.G.: Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys. Rev. A 85, 022311 (2012)

    Article  ADS  Google Scholar 

  87. Sheng, Y.B., Zhou, L., Zhao, S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012)

    Article  ADS  Google Scholar 

  88. Ren, B.C., Long, G.L.: General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities. Opt. Express 22, 6547 (2014)

    Article  ADS  Google Scholar 

  89. Gu, B.: Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics. J. Opt. Soc. Am. B 29, 1685–1689 (2012)

    Article  ADS  Google Scholar 

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Acknowledgments

This work is supported by Shaanxi Natural Science Foundation under Contract No.2013JM1009 and the Innovation Fund of graduate school of Xi’an University of Posts and Telecommunications under Contract No. ZL 2013-33.

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  1. School of Science, Xi’an University of Posts and Telecommunications, Xi’an, 710121, People’s Republic of China

    Bei Zhao, Xin-Wei Zha, Ya-Jun Duan & Xin-Mei Sun

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  1. Bei Zhao
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Zhao, B., Zha, XW., Duan, YJ. et al. An Efficient Scheme of Quantum Wireless Multi-hop Communication using Coefficient Matrix. Int J Theor Phys 54, 2977–2990 (2015). https://doi.org/10.1007/s10773-015-2537-y

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