Skip to main content
SpringerLink
Log in

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

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

Notes

  1. The Unruh effect itself may be in turn interpreted as a quantum noise channel of amplitude-damping type [21].

References

  1. Alonso-Sanz, R., Carvalho, M., Situ, H.: A quantum relativistic prisoner’s dilemma cellular automaton. Int. J. Theoretical Physics, (in press) (2016)

  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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quantum Inf. Process. 14(1), 147–164 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  4. Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. Proc. R. Soc. A 470, 20130793 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  5. Alonso-Sanz, R.: On a three-parameter quantum battle of the sexes cellular automaton. Quantum Inf. Process. 12(5), 1835–1850 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  6. Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. Proc. R. Soc. A 468, 3370–3383 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  7. Alonso-Sanz, R.: Dynamical Systems with Memory. World Scientific Pub. (2011)

  8. Alsing, P.M., Fuentes-Schuller, I., Mann, R.B., Tessier, T.E.: Phys. Rev. A 74, 032326 (2006)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  11. Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phys. Rev. Lett. 83(15), 3077–3080 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Flitney, A.P., Abbott, D.: Quantum games with decoherence. J. Phys A: Math. Gen. 38(2), 449 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Huang, Z.M., Qiu, D.: Quantum games under decoherence. Int. J. Theor. Phys. 55(2), 965–992 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  15. Huang, Z.M., Alonso-Sanz, R., Situ, H.Z.: Quantum Samaritan’s game under decoherence. Int. J. Theor. Phys. (submitted) (2016)

  16. Khan, S., Khan, M.K.: Noisy relativistic quantum games in noninertial frames 12(2), 1351–1363 (2013)

  17. Khan, S., Khan, M.K.: Relativistic quantum games in noninertial frames. J. Phys. A: Math. Theor. 44, 355302 (2011)

    Article  ADS  MATH  Google Scholar 

  18. Nawaz, A., Toor, A.H.: Dilemma and quantum battle of sexes. J. Phys. A: Math. Gen. 37(15), 4437–4443 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

  20. Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  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. Owen, G.: Game Theory. Academic Press (1995)

  23. Schiff, J.L.: Cellular automata: A discrete view of the world. Wiley (2008)

  24. Situ, H.Z., Huang, Z.M.: Relativistic quantum Bayesian game under decoherence. Int. J. Theor. Phys. 55, 2354–2363 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  25. Situ, H.Z: A quantum approach to play asymmetric coordination games. Quantum Inf. Process. 13, 591–599 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Situ, H.Z.: Quantum Bayesian game with symmetric and asymmetric information. Quantum Inf. Process. 14, 1827–1840 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Situ, H.Z.: Two-player conflicting interest Bayesian games and Bell nonlocality. Quantum Inf. Process. 15, 137–145 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  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. Takagi, S.: Prog. Theor. Phys.: Suppl. 88, 1 (1986)

    Article  ADS  Google Scholar 

  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

    Article  Google Scholar 

Download references

Acknowledgments

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. RAS contribution has been funded by the Spanish Grant MTM2015-63914-P. H. Situ’s contribution has been funded by the National Natural Science Foundation of China (Grant No. 61502179), the Natural Science Foundation of Guangdong Province of China (Grant No. 2014A030310265), and the China Scholarship Council.

Author information

Authors and Affiliations

  1. Technical University of Madrid, ETSIAAB (Estadistica, GSC). C.Universitaria., Madrid, 28040, Spain

    Ramón Alonso-Sanz

  2. College of Mathematics and Informatics, South China Agricultural University, Guangzhou, 510642, China

    Haozhen Situ

Authors
  1. Ramón Alonso-Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haozhen Situ
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ramón Alonso-Sanz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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, 5265–5279 (2016). https://doi.org/10.1007/s10773-016-3147-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-016-3147-z

Keywords

Search

Navigation