Advertisement

Open quantum walks

A mini review of the field and recent developments
  • Ilya SinayskiyEmail author
  • Francesco Petruccione
Review
  • 13 Downloads
Part of the following topical collections:
  1. Non-equilibrium Dynamics: Quantum Systems and Foundations of Quantum Mechanics

Abstract

Open quantum walks (OQWs) are a class of quantum walks, which are purely driven by the interaction with the dissipative environment. In this paper, we review theoretical advances on the foundations of discrete time OQWs, continuous time OQWs and a scaling limit of OQWs called open quantum Brownian motion. The main focus of the review is on the results and developments of discrete time OQW, covering general formalism, quantum trajectories for OQWs, central limit theorems, the microscopic derivation as well as possible generalisations and applications of OQWs.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    W. Feller, in An Introduction to Probability Theory and Its Applications (Wiley, New York 1968), Vol. 1 Google Scholar
  2. 2.
    Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48, 1687 (1993) ADSCrossRefGoogle Scholar
  3. 3.
    J. Kempe, Contemp. Phys. 44, 307 (2003) ADSCrossRefGoogle Scholar
  4. 4.
    S.E. Venegas-Andraca, Quantum Inf. Process. 11, 1015 (2012) MathSciNetCrossRefGoogle Scholar
  5. 5.
    S. Attal, F. Petruccione, C. Sabot, I. Sinayskiy, J. Stat. Phys. 147, 832 (2012) ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    S. Attal, F. Petruccione, I. Sinayskiy, Phys. Lett. A 376, 1545 (2012) ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    I. Sinayskiy, F. Petruccione, J. Phys.: Conf. Ser. 442, 012003 (2013) Google Scholar
  8. 8.
    S. Attal, N. Guillotin-Plantard, C. Sabot, Ann. Henri Poincaré 16, 15 (2015) ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    N. Konno, H.J. Yoo, J. Stat. Phys. 150, 299 (2013) ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    P. Sadowski, L. Pawela, Quantum Inf. Process. 15, 2725 (2016) ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    I. Sinayskiy, F. Petruccione, Phys. Scr. T151, 014077 (2012) ADSCrossRefGoogle Scholar
  12. 12.
    R. Carbone, Y. Pautrat, Ann. Henri Poincaré 17 99 (2016) ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    R. Carbone, Y. Pautrat, J. Stat. Phys. 160, 1125 (2015) ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    I. Bardet, D. Bernard, Y. Pautrat, J. Stat. Phys. 167, 173 (2017) ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    C.F. Lardizabal, R.R. Souza, J. Stat. Phys. 159, 772 (2015) ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    S. Gudder, Found. Phys. 39, 573 (2009) ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    S. Gudder, J. Math. Phys. 49, 072105 (2008) ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    C.F. Lardizabal, R.R. Souza, J. Stat. Phys. 164, 1122 (2016) ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    C.F. Lardizabal, Quantum Inf. Comput. 17, 79 (2017) MathSciNetGoogle Scholar
  20. 20.
    S.L. Carvalho, L.F. Guidi, C.F. Lardizabal, Quantum Inf. Process. 16, 17 (2017) ADSCrossRefGoogle Scholar
  21. 21.
    T.S. Jacq, C.F. Lardizabal, J. Stat. Phys. 169, 547 (2017) ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    A. Dhahri, F. Mukhamedov, https://doi.org/arXiv:1608.01065 (2016)
  23. 23.
    L. Accardi, Funct. Anal. Its Appl. 9, 1 (1975) CrossRefGoogle Scholar
  24. 24.
    F.A. Grünbaum, L. Velázquez, Adv. Math. 326, 352 (2018) MathSciNetCrossRefGoogle Scholar
  25. 25.
    S. Xiong, W.S. Yang, J. Stat. Phys. 152, 473 (2013) ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    L. Pawela, P. Gawron, J.A. Miszczak, P. Sadowski, PLoS One 10, 0130967 (2015) CrossRefGoogle Scholar
  27. 27.
    C. Wang, C. Wang, S. Ren, Y. Tang, Quantum Inf. Process. 17, 46 (2018) ADSCrossRefGoogle Scholar
  28. 28.
    C. Ampadu, Commun. Theor. Phys. 59, 563 (2013) MathSciNetCrossRefGoogle Scholar
  29. 29.
    C. Ampadu, Chin. Phys. B 23, 030302 (2014) CrossRefGoogle Scholar
  30. 30.
    C. Ampadu, SciFed J. Quantum Phys. 1, 1000006 (2017) Google Scholar
  31. 31.
  32. 32.
    C.F. Lardizabal, https://doi.org/arXiv:1801.09578 (2018)
  33. 33.
    I. Sinayskiy, F. Petruccione, Quantum Inf. Process. 11, 1301 (2012) MathSciNetCrossRefGoogle Scholar
  34. 34.
    B. Kraus, H.P. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller, Phys. Rev. A 78, 042307 (2008) ADSCrossRefGoogle Scholar
  35. 35.
    M.J. Kastoryano, F. Reiter, A.S. Sorensen, Phys. Rev. Lett. 106, 090502 (2011) ADSCrossRefGoogle Scholar
  36. 36.
    I. Sinaysky, F. Petruccione, D. Burgarth, Phys. Rev. A 78, 062301 (2008) ADSCrossRefGoogle Scholar
  37. 37.
    R. Sweke, I. Sinayskiy, F. Petruccione, J. Phys. B 46, 104004 (2013) ADSCrossRefGoogle Scholar
  38. 38.
    R. Sweke, I. Sinayskiy, F. Petruccione, Phys. Rev. A 87, 042323 (2013) ADSCrossRefGoogle Scholar
  39. 39.
    F. Verstraete, M.M. Wolf, J.I. Cirac, Nat. Phys. 5, 633 (2009) CrossRefGoogle Scholar
  40. 40.
    I. Sinayskiy, F. Petruccione, Int. J. Quantum Inform. 12, 14610101 (2014) CrossRefGoogle Scholar
  41. 41.
    I. Sinayskiy, F. Petruccione, Open Syst. Inf. Dyn. 20, 1340007 (2013) CrossRefGoogle Scholar
  42. 42.
    I. Sinayskiy, F. Petruccione, Phys. Rev. A 92, 032105 (2015) ADSMathSciNetCrossRefGoogle Scholar
  43. 43.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002) Google Scholar
  44. 44.
    E.B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976) Google Scholar
  45. 45.
    V. Gorini, A. Kossakowski, E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976) ADSCrossRefGoogle Scholar
  46. 46.
    G. Lindblad, Commun. Math. Phys. 48, 119 (1976) ADSCrossRefGoogle Scholar
  47. 47.
    C. Pellegrini, J. Stat. Phys. 154, 838 (2014) ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    H.P. Breuer, Phys. Rev. A 75, 022103 (2007) ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    S. Attal, Y. Pautrat, Ann. Henri Poincaré 7, 59 (2006) ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    H. Bringuier, Ann. Henri Poincaré 18, 3167 (2017) ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    C. Liu, R. Balu, Quantum Inf. Process. 16, 173 (2017) ADSCrossRefGoogle Scholar
  52. 52.
    I. Bardet, H. Bringuier, Y. Pautrat, C. Pellegrini, https://doi.org/arXiv:1803.03436 (2018)
  53. 53.
    M. Bauer, D. Bernard, A. Tilloy, Phys. Rev. A 88, 062340 (2013) ADSCrossRefGoogle Scholar
  54. 54.
    M. Bauer, D. Bernard, A. Tilloy, J. Stat. Mech. 2014, P09001 (2014) CrossRefGoogle Scholar
  55. 55.
    I. Sinayskiy, F. Petruccione, Phys. Scr. T165, 014017 (2015) ADSCrossRefGoogle Scholar
  56. 56.
    I. Sinayskiy, F. Petruccione, Fortschr. Phys. 65, 1600063 (2017) CrossRefGoogle Scholar

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Quantum Research Group, School of Chemistry and PhysicsDurban, KwaZulu-NatalSouth Africa
  2. 2.National Institute for Theoretical Physics (NITheP)KwaZulu-NatalSouth Africa
  3. 3.School of Electrical Engineering, KAISTDaejeonRepublic of Korea

Personalised recommendations