International Journal of Theoretical Physics

, Volume 55, Issue 12, pp 5265–5279 | Cite as

On the Effect of Quantum Noise in a Quantum-Relativistic Prisoner’s Dilemma Cellular Automaton

Article

Abstract

The disrupting effect of quantum noise on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.

Keywords

Quantum games Noise Unruh effect Cellular automata 

References

  1. 1.
    Alonso-Sanz, R., Carvalho, M., Situ, H.: A quantum relativistic prisoner’s dilemma cellular automaton. Int. J. Theoretical Physics, (in press) (2016)Google Scholar
  2. 2.
    Alonso-Sanz, R.: A cellular automaton implementation of a quantum battle of the sexes game with imperfect information. Quantum Inf. Process. 14(10), 3639–3659 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process. 14(1), 147–164 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. Proc. R. Soc. A 470, 20130793 (2014)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Alonso-Sanz, R.: On a three-parameter quantum battle of the sexes cellular automaton. Quantum Inf. Process. 12(5), 1835–1850 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. Proc. R. Soc. A 468, 3370–3383 (2012)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Alonso-Sanz, R.: Dynamical Systems with Memory. World Scientific Pub. (2011)Google Scholar
  8. 8.
    Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Phys. Rev. A 74, 032326 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    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)ADSMathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    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)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)ADSMathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Flitney, A.P., Abbott, D.: Advantage of a quantum player over a classical one in 2x2 quantum games. Proc. R. Soc. Lond. A 459(2038), 2463–2474 (2003)ADSMathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Flitney, A.P., Abbott, D.: Quantum games with decoherence. J. Phys A: Math. Gen. 38(2), 449 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Huang, Z.M., Qiu, D.: Quantum games under decoherence. Int. J. Theor. Phys. 55(2), 965–992 (2016)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Huang, Z.M., Alonso-Sanz, R., Situ, H.Z.: Quantum Samaritan’s game under decoherence. Int. J. Theor. Phys. (submitted) (2016)Google Scholar
  16. 16.
    Khan, S., Khan, M.K.: Noisy relativistic quantum games in noninertial frames 12(2), 1351–1363 (2013)Google Scholar
  17. 17.
    Khan, S., Khan, M.K.: Relativistic quantum games in noninertial frames. J. Phys. A: Math. Theor. 44, 355302 (2011)ADSCrossRefMATHGoogle Scholar
  18. 18.
    Nawaz, A., Toor, A.H.: Dilemma and quantum battle of sexes. J. Phys. A: Math. Gen. 37(15), 4437–4443 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Nawaz, A., Toor, A.H.: Generalized quantization scheme for two-person non-zero sum games. J. Phys. A: Math. Gen. 37(42), 365305 (2004)MathSciNetMATHGoogle Scholar
  20. 20.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  21. 21.
    Omkar, S., Srikanth, R., Banerjee, S., Alok, A.K.: The Unruh effect interpreted as a quantum noise channel. Quantum Inf. Comput. 9–10, 0757–0770 (2016)Google Scholar
  22. 22.
    Owen, G.: Game Theory. Academic Press (1995)Google Scholar
  23. 23.
    Schiff, J.L.: Cellular automata: A discrete view of the world. Wiley (2008)Google Scholar
  24. 24.
    Situ, H.Z., Huang, Z.M.: Relativistic quantum Bayesian game under decoherence. Int. J. Theor. Phys. 55, 2354–2363 (2016)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    Situ, H.Z: A quantum approach to play asymmetric coordination games. Quantum Inf. Process. 13, 591–599 (2014)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Situ, H.Z.: Quantum Bayesian game with symmetric and asymmetric information. Quantum Inf. Process. 14, 1827–1840 (2015)ADSMathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Situ, H.Z.: Two-player conflicting interest Bayesian games and Bell nonlocality. Quantum Inf. Process. 15, 137–145 (2016)ADSMathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    Situ, H.Z., Zhang, C., Yu, F.: Quantum advice enhances social optimality in three-party conflicting interest games. Quantum Inf. Comput. 16, 588–596 (2016)Google Scholar
  29. 29.
    Takagi, S.: Prog. Theor. Phys.: Suppl. 88, 1 (1986)ADSCrossRefGoogle Scholar
  30. 30.
    Weng, G., Yu, Y.: A quantum battle of the sexes in noninertial frame. J. Modern Phys. 5, 9 (2014). doi:10.4236/jmp.2014.59094 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Technical University of MadridMadridSpain
  2. 2.College of Mathematics and InformaticsSouth China Agricultural UniversityGuangzhouChina

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