Skip to main content
SpringerLink
Log in

Trojan Quantum Walks

  • Atomic Physics
  • Published:
Brazilian Journal of Physics Aims and scope Submit manuscript

Abstract

We investigate the transport properties and entanglement between spin and position of one-dimensional quantum walks starting from a qubit over position states following a delta-like (local state) and Gaussian (delocalized state) distributions. We find out that if the initial state is delocalized enough and a NOT gate reflects this state backwards, then the interference pattern extinguishes the position dispersion without preventing the propagation of the state. This effect allows the creation of a Trojan wave packet, a non-spreading and non-stationary double-peak quantum state.

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

Similar content being viewed by others

References

  1. J.P. Emery, F. Marzari, A. Morbidelli, L.M. French, T. Grav. The complex history of Trojan asteroids. Asteroids IV (University of Arizona Press, Tucson, 2015)

    Google Scholar 

  2. I. Bialynicki-Birula, M. Kaliński, J.H. Eberly, Lagrange Equilibrium Points in Celestial Mechanics and Nonspreading Wave Packets for Strongly Driven Rydberg Electrons. Phys. Rev. Lett. 73, 1777 (1994)

    Article  ADS  Google Scholar 

  3. B. Wyker, S. Ye, F.B. Dunning, S. Yoshida, C.O. Reinhold, J. Burgdörfer, Creating and transporting trojan wave packets. Phys. Rev. Lett. 108, 043001 (2012)

    Article  ADS  Google Scholar 

  4. Y. Aharonov, L. Davidovich, N. Zagury, Quantum random walks. Phys. Rev. A. 48, 1687 (1993)

    Article  ADS  Google Scholar 

  5. J. Kempe, Quantum random walks: an introductory overview. Contemp. Phys. 44, 307 (2003)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. N. Shenvi, J. Kempe, K.B. Whaley, Quantum random-walk search algorithm. Phys. Rev. A. 67, 052307 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. J.R. Busemeyer, Z. Wang, J.T. Townsend, Quantum dynamics of human decision-making. J. Math. Psychol. 50, 220 (2006)

    Article  MathSciNet  Google Scholar 

  11. G.S. Engel, T.R. Calhoun, E.L. Read, T.K. Ahn, T. Mančcal, Y.C. Cheng, R.E. Blankenship, G.R. Fleming, Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature. 446, 782 (2007)

    Article  ADS  Google Scholar 

  12. G. Di Molfetta, A. Pérez, Quantum walks as simulators of neutrino oscillations in a vacuum and matter. New J. Phys. 10, 103038 (2016)

    Article  Google Scholar 

  13. Y. Wang, Y. Shang, P. Xue, Generalized teleportation by quantum walks. Quantum Inf. Process. 16, 221 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  14. J. Wang, K. Manouchehri, Physical implementation of quantum walks. Springer (2013)

  15. M.A. Nielsen, I.L. Chuang, Quantum computation and quantum information. Cambridge University Press (2010)

  16. Z.J. Li, J.A. Izaac, J.B. Wang, Position-defect-induced reflection, trapping, transmission, and resonance in quantum walks. Phys. Rev. A. 87, 012314 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. A.C. Orthey, E.P.M. Amorim, Connecting spreading and entanglement in quantum walks. arXiv:1807.01361 (2018)

  19. A.C. Orthey, E.P.M. Amorim, Asymptotic entanglement in quantum walks from delocalized initial states. Quantum Inf. Process. 16, 224 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  20. G. Abal, R. Siri, A. Romanelli, R. Donangelo, Quantum walk on the line: entanglement and nonlocal initial conditions. Phys. Rev. A. 73, 042302 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  21. G. Abal, R. Siri, A. Romanelli, R. Donangelo, Erratum: Quantum walk on the line: entanglement and non-local initial conditions [phys. rev. a 73, 042302 (2006)]. Phys. Rev. A. 73, 069905(E) (2006)

    Article  ADS  Google Scholar 

  22. A. Kempf, R. Portugal, Group velocity of discrete-time quantum walks. Phys. Rev. A. 79, 052317 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  23. A.C. Orthey, E.P.M. Amorim, Weak disorder enhancing the production of entanglement in quantum walks. arXiv:1711.09246 (2018)

  24. R. Vieira, E.P.M. Amorim, G. Rigolin, Dynamically disordered quantum walk as a maximal entanglement generator. Phys. Rev. Lett. 111, 180503 (2013)

    Article  ADS  Google Scholar 

  25. R. Vieira, E.P.M. Amorim, G. Rigolin, Entangling power of disordered quantum walks. Phys. Rev. A. 89, 042307 (2014)

    Article  ADS  Google Scholar 

  26. A. Streltsov, U. Singh, H.S. Dhar, M.N. Bera, G. Adesso, Measuring quantum coherence with entanglement. Phys. Rev. Lett. 115, 020403 (2015)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

HSG and EPMA thank Janice Longo for her careful reading of the manuscript.

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001.

Author information

Authors and Affiliations

  1. Departamento de Física, Universidade do Estado de Santa Catarina, Joinville, SC, 89219-710, Brazil

    Henrique S. Ghizoni & Edgard P. M. Amorim

Authors
  1. Henrique S. Ghizoni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edgard P. M. Amorim
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Edgard P. M. Amorim.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghizoni, H.S., Amorim, E.P.M. Trojan Quantum Walks. Braz J Phys 49, 168–172 (2019). https://doi.org/10.1007/s13538-019-00638-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13538-019-00638-9

Keywords

Search

Navigation