Quantum Information Processing

, Volume 14, Issue 9, pp 3193–3210 | Cite as

Entanglement dynamics of two-particle quantum walks

  • G. R. Carson
  • T. Loke
  • J. B. Wang


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.


Quantum walk Entanglement dynamics Two-particle interaction Spectral analysis 



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


  1. 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)CrossRefADSGoogle Scholar
  2. 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)ADSGoogle Scholar
  3. 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)CrossRefADSGoogle Scholar
  4. 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)CrossRefADSGoogle Scholar
  5. 5.
    Fujisaki, H., Miyadera, T., Tanaka, A.: Dynamical aspects of quantum entanglement for weakly coupled kicked tops. Phys. Rev. E 67, 066201 (2003)MathSciNetCrossRefADSGoogle Scholar
  6. 6.
    Bandyopadhyay, J.N., Lakshminarayan, A.: Entanglement production in coupled chaotic systems: case of the kicked tops. Phys. Rev. E 69, 016201 (2004)MathSciNetCrossRefADSGoogle Scholar
  7. 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)MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    Hou, X.W., Hu, B.: Decoherence, entanglement, and chaos in the Dicke model. Phys. Rev. A 69, 042110 (2004)CrossRefADSGoogle Scholar
  9. 9.
    Lombardi, M., Matzkin, A.: Dynamical entanglement and chaos: the case of Rydberg molecules. Phys. Rev. A 73, 062335 (2006)CrossRefADSGoogle Scholar
  10. 10.
    Lombardi, M., Matzkin, A.: Scattering-induced dynamical entanglement and the quantum-classical correspondence. Europhys. Lett. 74, 771–777 (2006)MathSciNetCrossRefADSGoogle Scholar
  11. 11.
    Kempe, J.: Quantum random walks: an introductory overview. Contemp. Phys. 44(4), 307–327 (2003)MathSciNetCrossRefADSGoogle Scholar
  12. 12.
    Shenvi, N., Kempe, J., Whaley, K.B.: Quantum random-walk search algorithm. Phys. Rev. A 67, 052307 (2003)CrossRefADSGoogle Scholar
  13. 13.
    Reitzner, D., Hillery, M., Feldman, E., Buzek, V.: Quantum searches on highly symmetric graphs. Phys. Rev. A 79, 012323 (2009)CrossRefADSGoogle Scholar
  14. 14.
    Douglas, B.L., Wang, J.B.: A classical approach to the graph isomorphism problem using quantum walks. J. Phys. A 41, 075303 (2008)MathSciNetCrossRefADSGoogle Scholar
  15. 15.
    Berry, S.D., Wang, J.B.: Quantum-walk-based search and centrality. Phys. Rev. A 82, 042333 (2010)CrossRefADSGoogle Scholar
  16. 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)CrossRefGoogle Scholar
  17. 17.
    Mahasinghe, A., Wang, J.B., Wijerathna, J.K.: Quantum walk-based search and symmetries in graphs. J. Phys. A 47, 505301 (2014)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Manouchehri, K., Wang, J.B.: Physical Implementation of Quantum Walks. Springer, Berlin (2014)zbMATHCrossRefGoogle Scholar
  19. 19.
    Omar, Y., Paunković, N., Sheridan, L., Bose, S.: Quantum walk on a line with two entangled particles. Phys. Rev. A 74, 042304 (2006)MathSciNetCrossRefADSGoogle Scholar
  20. 20.
    Štefaňnák, M., Kiss, T., Jex, I., Mohring, B.: The meeting problem in the quantum walk. J. Phys. A 39(48), 14965–14983 (2006)MathSciNetCrossRefADSGoogle Scholar
  21. 21.
    Pathak, P.K., Agarwal, G.S.: Quantum random walk of two photons in separable and entangled states. Phys. Rev. A 75, 032351 (2007)MathSciNetCrossRefADSGoogle Scholar
  22. 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)CrossRefADSGoogle Scholar
  23. 23.
    Venegas-Andraca, S. E., Bose, S.: Quantum-walk-based generation of entanglement between two walkers. arXiv:0901.3946v1 [quant-ph]
  24. 24.
    Berry, S.D., Wang, J.B.: Two-particle quantum walks: entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011)CrossRefADSGoogle Scholar
  25. 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)CrossRefADSGoogle Scholar
  26. 26.
    Mintert, F., Carvalho, A.R.R., Kus, M., Buchleitner, A.: Measures and dynamics of entangled states. Phys. Rep. 415, 207–259 (2005)MathSciNetCrossRefADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of PhysicsThe University of Western AustraliaCrawleyAustralia

Personalised recommendations