Skip to main content
SpringerLink
Log in

Entanglement dynamics of two-particle quantum walks

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

This paper explores the entanglement dynamics generated by interacting two-particle quantum walks on degree-regular and degree-irregular graphs. We performed spectral analysis of the time-evolution of both the particle probability distribution and the entanglement between the two particles for various interaction strength. While the particle probability distributions are stable and not sensitive to perturbations in the interaction strength, the entanglement dynamics are found to be much more sensitive to system variations. This property may be utilised to probe small differences in the system parameters.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. Furuya, K., Nemes, M.C., Pellegrino, G.Q.: Quantum dynamical manifestation of chaotic behavior in the process of entanglement. Phys. Rev. Lett. 80, 5524–5527 (1999)

    Article  ADS  Google Scholar 

  2. Angelo, R.M., Furuya, K., Nemes, M.C., Pellegrino, G.Q.: Rapid decoherence in integrable systems: a border effect. Phys. Rev. A 60, 5407–5411 (1999)

    ADS  Google Scholar 

  3. Angelo, R.M., Furuya, K., Nemes, M.C., Pellegrino, G.Q.: Recoherence in the entanglement dynamics and classical orbits in the N-atom Jaynes–Cummings model. Phys. Rev. A 64, 043801 (2001)

    Article  ADS  Google Scholar 

  4. Miller, P.A., Sarkar, S.: Signatures of chaos in the entanglement of two coupled quantum kicked tops. Phys. Rev. E 60, 1542–1550 (1999)

    Article  ADS  Google Scholar 

  5. Fujisaki, H., Miyadera, T., Tanaka, A.: Dynamical aspects of quantum entanglement for weakly coupled kicked tops. Phys. Rev. E 67, 066201 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  6. Bandyopadhyay, J.N., Lakshminarayan, A.: Entanglement production in coupled chaotic systems: case of the kicked tops. Phys. Rev. E 69, 016201 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  7. Kubotani, H., Adachi, S., Toda, M.: Exact formula of the distribution of Schmidt eigenvalues for dynamical formation of entanglement in quantum chaos. Phys. Rev. Lett. 100, 240501 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  8. Hou, X.W., Hu, B.: Decoherence, entanglement, and chaos in the Dicke model. Phys. Rev. A 69, 042110 (2004)

    Article  ADS  Google Scholar 

  9. Lombardi, M., Matzkin, A.: Dynamical entanglement and chaos: the case of Rydberg molecules. Phys. Rev. A 73, 062335 (2006)

    Article  ADS  Google Scholar 

  10. Lombardi, M., Matzkin, A.: Scattering-induced dynamical entanglement and the quantum-classical correspondence. Europhys. Lett. 74, 771–777 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  11. Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44(4), 307–327 (2003)

    Article  MathSciNet  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Reitzner, D., Hillery, M., Feldman, E., Buzek, V.: Quantum searches on highly symmetric graphs. Phys. Rev. A 79, 012323 (2009)

    Article  ADS  Google Scholar 

  14. Douglas, B.L., Wang, J.B.: A classical approach to the graph isomorphism problem using quantum walks. J. Phys. A 41, 075303 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  15. Berry, S.D., Wang, J.B.: Quantum-walk-based search and centrality. Phys. Rev. A 82, 042333 (2010)

    Article  ADS  Google Scholar 

  16. Smith, J., Mosca, M.: Handbook of natural computing. In: Rozenberg, G., Bck, T., Kok, J.N. (eds.) Algorithms for Quantum Computers. Springer, Berlin (2012)

    Chapter  Google Scholar 

  17. Mahasinghe, A., Wang, J.B., Wijerathna, J.K.: Quantum walk-based search and symmetries in graphs. J. Phys. A 47, 505301 (2014)

    Article  MathSciNet  Google Scholar 

  18. Manouchehri, K., Wang, J.B.: Physical Implementation of Quantum Walks. Springer, Berlin (2014)

    Book  MATH  Google Scholar 

  19. Omar, Y., Paunković, N., Sheridan, L., Bose, S.: Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  20. Štefaňnák, M., Kiss, T., Jex, I., Mohring, B.: The meeting problem in the quantum walk. J. Phys. A 39(48), 14965–14983 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  21. Pathak, P.K., Agarwal, G.S.: Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75, 032351 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  22. Rohde, P.P., Fedrizzi, A., Ralph, T.C.: Entanglement dynamics and quasi-periodicity in discrete random walks. J. Mod. Opt. 59, 710–720 (2012)

    Article  ADS  Google Scholar 

  23. Venegas-Andraca, S. E., Bose, S.: Quantum-walk-based generation of entanglement between two walkers. arXiv:0901.3946v1 [quant-ph]

  24. Berry, S.D., Wang, J.B.: Two-particle quantum walks: entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011)

    Article  ADS  Google Scholar 

  25. Rohde, P.P., Fedrizzi, A., Ralph, T.C.: Entanglement dynamics and quasi-periodicity in discrete quantum walks. J. Mod. Opt. 59, 710–720 (2012)

    Article  ADS  Google Scholar 

  26. Mintert, F., Carvalho, A.R.R., Kus, M., Buchleitner, A.: Measures and dynamics of entangled states. Phys. Rep. 415, 207–259 (2005)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank Lock Yue Chew and Michael Small for several valuable discussions on the characterisation of nonlinear dynamics.

Author information

Authors and Affiliations

  1. School of Physics, The University of Western Australia, Crawley, WA, 6009, Australia

    G. R. Carson, T. Loke & J. B. Wang

Authors
  1. G. R. Carson
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Loke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. B. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. B. Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Carson, G.R., Loke, T. & Wang, J.B. Entanglement dynamics of two-particle quantum walks. Quantum Inf Process 14, 3193–3210 (2015). https://doi.org/10.1007/s11128-015-1047-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-015-1047-4

Keywords

Search

Navigation