Skip to main content
SpringerLink
Log in

Quantum Samaritan’s Dilemma Under Decoherence

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

Abstract

We study how quantum noise affects the solution of quantum Samaritan’s dilemma. Serval most common dissipative and nondissipative noise channels are considered as the model of the decoherence process. We find that the solution of quantum Samaritan’s dilemma is stable under the influence of the amplitude damping, the bit flip and the bit-phase flip channel.

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

Similar content being viewed by others

References

  1. Myerson, R.B.: Game theory: Analysis of conflict. Havard University Press, Boston (1991)

    MATH  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Eisert, J., Wilkens, M.: Quantum games. J. Mod. Opt. 47, 2543 (2000)

    Article  ADS  MATH  Google Scholar 

  4. Benjamin, S.C., Hayden, P.M.: Comment on “Quantum Games and Quantum Strategies”. Phys. Rev. Lett. 87, 069801 (2001)

    Article  ADS  Google Scholar 

  5. Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301 (2001)

    Article  ADS  Google Scholar 

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

    Article  ADS  MATH  Google Scholar 

  7. Situ, H.Z.: A quantum approach to play asymmetric coordination games. Quant. Inf. Process. 13, 591 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Fra̧ckiewicz, P.: A new quantum scheme for normal-form games. Quant. Inf. Process. 14, 1809 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  9. Fra̧ckiewicz, P.: Remarks on quantum duopoly schemes. Quant. Inf. Process. 15, 121 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  10. Weng, G.F., Yu, Y.: Playing quantum games by a scheme with pre- and post-selection. Quant. Inf. Process. 15, 147 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Khan, S., Khan, M.K.: Quantum Stackelberg duopoly in a noninertial frame. Chinese Phys. Lett. 28, 070202 (2011)

    Article  Google Scholar 

  12. Fra̧ckiewicz, P.: Quantum signaling game. J. Phys. A - Math. Theor. 47, 305301 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  13. Fra̧ckiewicz, P., Sładkowski, J.: Quantum information approach to the ultimatum game. Int. J. Theor. Phys. 53, 3248 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fra̧ckiewicz, P.: On signaling games with quantum chance move. J. Phys. A - Math. Theor. 48, 075303 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  15. Anand, N., Benjamin, C.: Do quantum strategies always win?. Quant. Inf. Process. 14, 4027 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  16. Iqbal, A., Abbott, D.: Quantum matching pennies game. J. Phys. Soc. Jpn. 78, 014803 (2009)

    Article  ADS  Google Scholar 

  17. Brunner, N., Linden, N.: Connection between Bell nonlocality and Bayesian game theory. Nat. Commun. 4, 2057 (2013)

    ADS  Google Scholar 

  18. Iqbal, A., Chappell, J.M., Li, Q., Pearce, C.E.M., Abbott, D.: A probabilistic approach to quantum Bayesian games of incomplete information. Quant. Inf. Process. 13, 2783 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Pappa, A., Kumar, N., Lawson, T., Santha, M., Zhang, S.Y., Diamanti, E., Kerenidis, I.: Nonlocality and conflicting interest games. Phys. Rev. Lett. 114, 020401 (2015)

    Article  ADS  Google Scholar 

  20. Iqbal, A., Chappell, J.M., Abbott, D.: Social optimality in quantum Bayesian games. Phys. A 436, 798 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Situ, H.Z.: Two-player conflicting interest Bayesian games and Bell nonlocality. Quant. Inf. Process. 15, 137 (2016)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  24. Khan, S., Ramzan, M., Khan, M.K.: Decoherence effects on multiplayer cooperative quantum games. Commun. Theor. Phys. 56, 228 (2011)

    Article  MATH  Google Scholar 

  25. Fra̧ckiewicz, P.: N-person quantum Russian roulette. Phys. A 401, 8 (2014)

    Article  MathSciNet  Google Scholar 

  26. Liao, X.P., Ding, X.Z., Fang, M.F.: Improving the payoffs of cooperators in three-player cooperative game using weak measurements. Quant. Inf. Process. 14, 4395 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  27. Situ, H.Z., Zhang, C., Yu, F.: Quantum advice enhances social optimality in three-party conflicting interest games. Quantum Inf. Comput. 16, 588 (2016)

    MathSciNet  Google Scholar 

  28. Alonso-Sanz, R.: A quantum battle of the sexes cellular automaton. P. Roy. Soc. A - Math. Phy. 468, 3370 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Alonso-Sanz, R.: A quantum prisoner’s dilemma cellular automaton. P. Roy. Soc. A - Math. Phy. 470, 20130793 (2014)

    Article  MathSciNet  Google Scholar 

  31. Alonso-Sanz, R.: Variable entangling in a quantum prisoner’s dilemma cellular automaton. Quant. Inf. Process. 14, 147 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  32. Alonso-Sanz, R.: A cellular automaton implementation of a quantum battle of the sexes game with imperfect information. Quant. Inf. Process. 14, 3639 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  33. Ozdemir, S.K., Shimamura, J., Morikoshi, F., Imoto, N.: Dynamics of a discoordination game with classical and quantum correlations. Phys. Lett. A 333, 218 (2004)

    Article  ADS  MATH  Google Scholar 

  34. Flitney, A.P., Abbott, D.: Quantum games with decoherence. J. Phys. A: Math. Gen. 38, 449 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  35. Nawaz, A., Toor, A.H.: Quantum games with correlated noise. J. Phys. A: Math. Gen. 39, 9321 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. Khan, S., Ramzan, M., Khan, M.K.: Quantum Stackelberg duopoly in the presence of correlated noise. J. Phys. A: Math. Theor. 43, 375301 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  37. Khan, S., Khan, M.K.: Noisy relativistic quantum games in noninertial frames. Quant. Inf. Process. 12, 1351 (2013)

    Article  ADS  MATH  Google Scholar 

  38. Ramzan, M.: Three-player quantum Kolkata restaurant problem under decoherence. Quant. Inf. Process 12, 577 (2013)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  39. Ramzan, M., Khan, M.K.: Environment-assisted quantum minority games. Fluct. Noise Lett. 12, 1350025 (2013)

    Article  Google Scholar 

  40. Gawron, P., Kurzyk, D., Pawela, L.: Decoherence effects in the quantum qubit flip game using Markovian approximation. Quant. Inf. Process. 13, 665 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  41. Huang, Z.M., Qiu, D.W.: Quantum games under decoherence. Int. J. Theor. Phys. 55, 965 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  42. Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

Download references

Acknowledgments

We are very grateful to the reviewers and the editors for their invaluable comments and detailed suggestions that helped to improve the quality of the present paper. This work is supported by the National Natural Science Foundation of China (Grant Nos. 61502179, 61472452), the Natural Science Foundation of Guangdong Province of China (Grant No. 2014A030310265), Guangdong Province Office of Education (Grant No. 2014KTSCX130), the Science Foundation for Young Teachers of Wuyi University (Grant No. 2015zk01), the Spanish Grant MTM2015-63914-P. H.Z. Situ is sponsored by the State Scholarship Fund of the China Scholarship Council.

Author information

Authors and Affiliations

  1. School of Economics and Management, Wuyi University, Jiangmen, 529020, China

    Zhiming Huang

  2. Technical University of Madrid, ETSIA (Estadística, GSC). C.Universitaria, Madrid, 28040, Spain

    Ramón Alonso-Sanz

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

    Haozhen Situ

Authors
  1. Zhiming Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ramón Alonso-Sanz
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haozhen Situ
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Haozhen Situ.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, Z., Alonso-Sanz, R. & Situ, H. Quantum Samaritan’s Dilemma Under Decoherence. Int J Theor Phys 56, 863–873 (2017). https://doi.org/10.1007/s10773-016-3229-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-016-3229-y

Keywords

Search

Navigation