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Discord and entanglement of two-particle quantum walk on cycle graphs

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Abstract

In this paper, we investigate the dynamics of quantum discord and entanglement between the coin states of two quantum walkers on cycle graphs of various size in discrete time. For a few special cycle sizes, we obtained analytical solutions showing the origin of perfect periodic recurrence of quantum discord and entanglement. We found that the time evolution of such quantum correlations becomes increasingly complex when we introduce local interactions between the two walkers by applying an additional phase to the coin operator when they are at the same node. The effects of the interaction strength on the dynamics of the quantum discord and entanglement are studied in detail.

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References

  1. Berry, S.D., Wang, J.B.: Two-particle quantum walks: Entanglement and graph isomorphism testing. Phys. Rev. A 83, 042317 (2011). doi:10.1103/PhysRevA.83.042317

    Article  ADS  Google Scholar 

  2. Datta, A., Shaji, A., Caves, C.M.: Quantum discord and the power of one qubit. Phys. Rev. Lett. 050502 (2008). doi:10.1103/PhysRevLett.100.050502

  3. Douglas, B.L., Wang, J.B.: Efficient quantum circuit implementation of quantum walks. Phys. Rev. A 79, 052335 (2009). doi:10.1103/PhysRevA.79.052335

    Article  ADS  Google Scholar 

  4. Gamble, J.K., Friesen, M., Zhou, D., Joynt, R., Coppersmith, S.N.: Two-particle quantum walks applied to the graph isomorphism problem. Phys. Rev. A 81(5), 052313 (2010). doi:10.1103/PhysRevA.81.052313

    Article  ADS  Google Scholar 

  5. Lang, M.D., Caves, C.M.: Quantum discord and the geometry of bell-diagonal states. Phys. Rev. Lett. 105, 150501 (2010). doi:10.1103/PhysRevLett.105.150501

  6. Loke, T., Wang, J.B.: Efficient circuit implementation of quantum walks on non-degree-regular graphs. Phys. Rev. A 86, 042338 (2012). doi:10.1103/PhysRevA.86.042338

    Article  ADS  Google Scholar 

  7. Luo, S.: Quantum discord for two-qubit systems. Phys. Rev. A 77, 042303 (2008). doi:10.1103/PhysRevA.77.042303

    Article  ADS  Google Scholar 

  8. Manouchehri, K., Wang, J.B.: Quantum walks in an array of quantum dots. J. Phys. A 41, 065304 (2008). doi:10.1088/1751-8113/41/6/065304

    Article  ADS  MathSciNet  Google Scholar 

  9. Manouchehri, K., Wang, J.B.: Quantum random walks without walking. Phys. Rev. A 80, 060304 (2009). doi:10.1103/PhysRevA.80.060304

    Article  ADS  MathSciNet  Google Scholar 

  10. Manouchehri, K., Wang, J.B.: Physical Implementation of Quantum Walks. Springer, Berlin (2014). doi:10.1007/978-3-642-36014-5

    Book  MATH  Google Scholar 

  11. Matthews, J.C.F., Thompson, M.G.: Quantum optics: an entangled walk of photons. Nature 484, 7392 (2012). doi:10.1038/nature11035

    Google Scholar 

  12. Merali, Z.: The power of discord. Nature 474, 24 (2011). doi:10.1038/474024a

    Article  ADS  Google Scholar 

  13. Ollivier, H., Zurek, W.H.: Quantum discord: a measure of the quantumness of correlations. Phys. Rev. Lett. 88(1) (2002). doi:10.1103/PhysRevLett.88.017901

  14. Parashar, P., Rana, S.: Entanglement and discord of the superposition of Greenberger–Horne–Zeilinger states. Phys. Rev. A 83, 032301 (2011). doi:10.1103/PhysRevA.83.032301

    Article  ADS  Google Scholar 

  15. Peruzzo, A., Lobino, M., Matthews, J.C.F., Matsuda, N., Politi, A., Poulios, K., Zhou, X., Lahini, Y., Ismail, N., Bromberg, Y., Wrhoff, K., Silberberg, Y., Thompson, M.G., O’Brien, J.L.: Quantum walks of correlated photons. Science 329, 1193515 (2010). doi:10.1126/science.1193515

    Article  Google Scholar 

  16. Rao, B.R., Srikanth, R., Chandrashekar, C.M., Banerjee, S.: Quantumness of noisy quantum walks: a comparison between measurement-induced disturbance and quantum discord. Phys. Rev. A 83, 064302 (2011). doi:10.1103/PhysRevA.81.062123

    Article  ADS  Google Scholar 

  17. Sarandy, M.S.: Classical correlation and quantum discord in critical systems. Phys. Rev. A 80, 022108 (2009). doi:10.1103/PhysRevA.80.022108

    Article  ADS  Google Scholar 

  18. Tregenna, B., Flanagan, W., Maile, R., Kendon, V.: Controlling discrete quantum walks: coins and initial states. New Journal of Physics 5, 83 (2003). doi:10.1088/1367-2630/5/1/383

    Article  ADS  Google Scholar 

  19. Wootters, W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 10 (1998). doi:10.1103/PhysRevLett.80.2245

  20. Xue, P., Sanders, B.C.: Two quantum walkers sharing coins. Phys. Rev. A 85, 022307 (2012). doi:10.1103/PhysRevA.85.022307

    Article  ADS  Google Scholar 

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Acknowledgments

The authors would like to thank Chris Murphy for his earlier involvement in this project. Thanks are also due to Shaoming Fei, Shunlong Luo and Thomas Loke for several valuable discussions, and Bruce Hartley for proof reading.

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Authors and Affiliations

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

    J. P. J. Rodriguez, Z. J. Li & J. B. Wang

  2. Institute of Theoretical Physics, Shanxi University, Taiyuan, 030006, China

    Z. J. Li

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  1. J. P. J. Rodriguez
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  2. Z. J. Li
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  3. J. B. Wang
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Correspondence to J. B. Wang.

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Rodriguez, J.P.J., Li, Z.J. & Wang, J.B. Discord and entanglement of two-particle quantum walk on cycle graphs. Quantum Inf Process 14, 119–133 (2015). https://doi.org/10.1007/s11128-014-0859-y

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  • DOI: https://doi.org/10.1007/s11128-014-0859-y

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