Advertisement

On the effect of memory in a quantum prisoner’s dilemma cellular automaton

  • Ramón Alonso-Sanz
  • Fabio Revuelta
Article
  • 119 Downloads

Abstract

The disrupting effect of quantum memory on the dynamics of a spatial quantum formulation of the iterated prisoner’s dilemma game with variable entangling is studied. The game is played within a cellular automata framework, i.e., with local and synchronous interactions. The main findings of this work refer to the shrinking effect of memory on the disruption induced by noise.

Keywords

Memory Quantum games Cellular automata 

Notes

Acknowledgements

This work has been funded by the Spanish Grant MTM2015-63914-P. Part of the computations of this work were performed in EOLO, an HPC machine of the International Campus of Excellence of Moncloa, funded by the UCM and Feder Funds.

References

  1. 1.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Alonso-Sanz, R.: On a three-parameter quantum battle of the sexes cellular automaton. Quantum Inf. Process. 12(5), 1835–1850 (2013)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. Proc. R. Soc. A 468, 3370–3383 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Huang, Z., Alonso-Sanz, R., Situ, H.: Quantum Samaritan’s dilemma under decoherence. Int. J. Theor. Phys. 56(3), 863–873 (2017)CrossRefzbMATHGoogle Scholar
  5. 5.
    Alonso-Sanz, R., Situ, H.: A quantum Samaritan’s dilemma cellular automaton. R. Soc. Open Sci. 4(6), 863–160669 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Ozdemir, S.K., Shimamura, J., Morikoshi, F., Imoto, N.: Dynamics of a discoordination game with classical and quantum correlations. Phys. Lett. A 333, 218–231 (2004)ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Du, J.F., Li, H., Xu, X., Shi, M., Wi, J., Zhou, X., Han, R.: Experimental realization of quantum games on a quantum computer. Phys. Rev. Lett. 88(13), 137902 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  9. 9.
    Ramzan, M., Nawaz, A., Toor, A.H., Khan, M.K.: The effect of quantum memory on quantum games. J. Phys. A Math. Theor. 41, 055307 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Owen, G.: Game Theory. Academic Press, Cambridge (1995)zbMATHGoogle Scholar
  11. 11.
    Benjamin, S.C., Hayden, P.M.: Comment on “Quantum games and quantum strategies”. Phys. Rev. Lett. 87, 069801 (2001)ADSCrossRefGoogle Scholar
  12. 12.
    Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    Eisert, J., Wilkens, M., Lewenstein, M.: Comment on “Quantum games and quantum strategies”—reply. Phys. Rev. Lett. 87, 069802 (2001)ADSCrossRefGoogle Scholar
  14. 14.
    Eisert, J., Wilkens, M.: Quantum games. J. Mod. Opt. 47(14–15), 2543–2556 (2000)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Alonso-Sanz, R.: Spatial correlated games. R. Soc. Open Sci. 4(6), 171361 (2017).  https://doi.org/10.1098/rsos.171361 CrossRefGoogle Scholar
  16. 16.
    Zhang, S. (2012). Quantum strategic game theory. In: Proceedings of the 3rd Innovations in Theoretical Computer Science Conference (ITCS ’12). ACM, New York. ISBN: 978-1-4503-1115-1Google Scholar
  17. 17.
    Brunner, N., Linden, N.: Connection between nonlocality and Bayesian game theory. Nat. Commun. 4, 2057 (2013)ADSGoogle Scholar
  18. 18.
    Pappa, A., Kumar, N., Lawson, T., Santha, M., Zhang, S., Diamanti, E., Kerenidis, I.: Nonlocality and conflicting interest games. Phys. Rev. Lett. 114, 020401 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    Yin, J., et al.: Satellite-based entanglement distribution over 1200 kilometers. Science 356, 1140 (2017)CrossRefGoogle Scholar
  20. 20.
    Schiff, J.L.: Cellular Automata: A Discrete View of the World. Wiley, London (2008)zbMATHGoogle Scholar
  21. 21.
    Du, J.F., Xu, X.D., Li, H., Zhou, X., Han, R.: Entanglement playing a dominating role in quantum games. Phys. Lett. A 89(1–2), 9–15 (2001)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Du, J.F., Li, H., Xu, X.D., Zhou, X., Han, R.: Phase-transition-like behaviour of quantum games. J. Phys. A Math. Gen. 36(23), 6551–6562 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Alonso-Sanz, R.: On the effect of quantum noise in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process. 16(6), 161 (2017)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process. 14(1), 147–164 (2015)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. Proc. R. Soc. A 470, 20130793 (2014)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Flitney, A.P., Abbott, D.: Advantage of a quantum player over a classical one in \(2\times 2\) quantum games. Proc. R. Soc. Lond. A 459(2038), 2463–2474 (2003)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Flitney, A.P., Abbott, D.: Quantum games with decoherence. J. Phys. A Math. Gen. 38(2), 449 (2004)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Alonso-Sanz, R., Situ, H.: On the effect of quantum noise in a quantum relativistic prisoner’s dilemma cellular automaton. Int. J. Theor. Phys. 55(12), 5265–5279 (2016)CrossRefzbMATHGoogle Scholar
  29. 29.
    Alonso-Sanz, R., Situ, H.: On the effect of quantum noise in a quantum relativistic battle of the sexes cellular automaton. Phys. A 468, 267–277 (2016)CrossRefzbMATHGoogle Scholar
  30. 30.
    Alonso-Sanz, R.: Dynamical Systems with Memory. World Scientific, Singapore (2011)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Grupo de Sistemas Complejos, ETSIAABUniversidad Politécnica de MadridMadridSpain
  2. 2.Instituto de Ciencias Matemáticas (ICMAT)MadridSpain

Personalised recommendations