Skip to main content
SpringerLink
Log in

Generalized teleportation by quantum walks

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We develop a generalized teleportation scheme based on quantum walks with two coins. For an unknown qubit state, we use two-step quantum walks on the line and quantum walks on the cycle with four vertices for teleportation. For any d-dimensional states, quantum walks on complete graphs and quantum walks on d-regular graphs can be used for implementing teleportation. Compared with existing d-dimensional states teleportation, prior entangled state is not required and the necessary maximal entanglement resource is generated by the first step of quantum walk. Moreover, two projective measurements with d elements are needed by quantum walks on the complete graph, rather than one joint measurement with \(d^2\) basis states. Quantum walks have many applications in quantum computation and quantum simulations. This is the first scheme of realizing communicating protocol with quantum walks, thus opening wider applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Venegas-Andraca, S.E.: Quantum walks: a comprehensive review. Quantum Inf. Process. 11, 1015C1106 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Ambainis, A., et al.: One-dimensional quantum walks. In: Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing, pp. 37–49 (2001)

  3. Aharonov, D., Ambainis, A., Kempe, J, Vazirani, U.: Quantum walks on graphs. In: Proceedings of the Thirty-third Annual ACM Symposium on Theory of Computing, p. 50 (2001)

  4. Ambainis, A.: Quantum walk algorithm for element distinctness. SIAM J. Comput. 37, 210 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Childs, A.M.: Universal computation by quantum walk. Phys. Rev. Lett. 102, 180501 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. Childs, A.M., Gosset, D., Webb, Z.: Universal computation by multiparticle quantum walk. Science 339, 791 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Lovett, N.B., Cooper, S., Everitt, M., Trevers, M., Kendon, V.: Universal quantum computation using the discrete-time quantum walk. Phys. Rev. A 81, 042330 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  8. Kurzyński, P., Wójcik, A.: Quantum walk as a generalized measuring device. Phys. Rev. Lett. 110, 200404 (2013)

    Article  ADS  Google Scholar 

  9. Travaglione, B.C., Milburn, G.J.: Implementing the quantum random walk. Phys. Rev. A 65, 032310 (2002)

    Article  ADS  Google Scholar 

  10. Sanders, B.C., Bartlett, S.D., Tregenna, B., Knight, P.L.: Quantum quincunx in cavity quantum electrodynamics. Phys. Rev. A 67, 042305 (2003)

    Article  ADS  Google Scholar 

  11. Dür, W., Raussendorf, R., Kendon, V.M., Briegel, H.J.: Quantum walks in optical lattices. Phys. Rev. A 66, 052319 (2002)

    Article  ADS  Google Scholar 

  12. Xue, P., Sanders, B.C., Leibfried, D.: Quantum walk on a line for a trapped ion. Phys. Rev. Lett. 103, 183602 (2009)

    Article  ADS  Google Scholar 

  13. Schreiber, A., et al.: Photons walking the line: a quantum walk with adjustable coin operations. Phys. Rev. Lett. 104, 050502 (2010)

    Article  ADS  Google Scholar 

  14. Goyal, S.K., Roux, F.S., Forbes, A., Konrad, T.: Implementing quantum walks using orbital angular momentum of classical light. Phys. Rev. Lett. 110, 263602 (2013)

    Article  ADS  Google Scholar 

  15. Brun, T.A., Carteret, H.A., Ambainis, A.: Quantum walks driven by many coins. Phys. Rev. A 67, 052317 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  16. Bennett, C.H., et al.: Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Zhou, X., Leung, D.W., Chuang, I.L.: Methodology for quantum logic gate construction. Phys. Rev. A 62, 052316 (2000)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are very thankful for the anonymous reviewers for their thoughtful suggestions, which helped us improve this paper substantially. This work was partially supported by the National Key Research and Development Program of China under Grant 2016YFB1000902, National Research Foundation of China (Grant No. 61472412), Program for Creative Research Group of National Natural Science Foundation of China (Grant No. 61621003). This work has been supported by NSFC (Nos. 11474049 and 11674056), NSFJS (No. BK20160024) and the Open Fund from State Key Laboratory of Precision Spectroscopy, East China Normal University.

Author information

Authors and Affiliations

  1. Institute of Mathematics, AMSS, CAS, Beijing, 100190, China

    Yu Wang & Yun Shang

  2. NCMIS, AMSS, CAS, Beijing, 100190, China

    Yun Shang

  3. Department of Physics, Southeast University, Nanjing, 211189, China

    Peng Xue

  4. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, China

    Yu Wang & Yun Shang

Authors
  1. Yu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun Shang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Xue
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yun Shang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Shang, Y. & Xue, P. Generalized teleportation by quantum walks. Quantum Inf Process 16, 221 (2017). https://doi.org/10.1007/s11128-017-1675-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-017-1675-y

Keywords

Search

Navigation