Skip to main content
Erschienen in: Quantum Information Processing 12/2015

01.12.2015

Improving the payoffs of cooperators in three-player cooperative game using weak measurements

verfasst von: Xiang-Ping Liao, Xiang-Zhuo Ding, Mao-Fa Fang

Erschienen in: Quantum Information Processing | Ausgabe 12/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this paper, an efficient method is proposed to improve the payoffs of cooperators in cooperative three-player quantum game under the action of amplitude damping, bit flip and depolarizing channels using weak measurements. It is shown that the payoffs of cooperators can be enhanced to a great extent in the case of amplitude damping channel, and the payoff sudden death can be avoided in the case of bit flip and depolarizing channels. Moreover, the payoffs of cooperators tend to a constant by changing weak measurement strength in spite of sufficiently strong decoherence.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Zurück zum Zitat von-Neumann, J., Morgenstein, O.: The Theory of Games and Economic Behaviour. Princeton University Press, Princeton, NJ (1944) von-Neumann, J., Morgenstein, O.: The Theory of Games and Economic Behaviour. Princeton University Press, Princeton, NJ (1944)
7.
Zurück zum Zitat Cheon, T., Iqbal, A.: Bayesian Nash equilibria and Bell inequalities. J. Phys. Soc. Jpn. 77, 024801 (2008)CrossRefADS Cheon, T., Iqbal, A.: Bayesian Nash equilibria and Bell inequalities. J. Phys. Soc. Jpn. 77, 024801 (2008)CrossRefADS
8.
Zurück zum Zitat Iqbal, A., Abbott, D.: Quantum matching pennies game. J. Phy. Soc. Jpn. 78, 014803 (2009)CrossRefADS Iqbal, A., Abbott, D.: Quantum matching pennies game. J. Phy. Soc. Jpn. 78, 014803 (2009)CrossRefADS
9.
Zurück zum Zitat Iqbal, A., Cheon, T., Abbott, D.: Probabilistic analysis of three-player symmetric quantum games played using the Einstein–Podolsky–Rosen–Bohm setting. Phys. Lett. A 372, 6564 (2008)MathSciNetCrossRefADSMATH Iqbal, A., Cheon, T., Abbott, D.: Probabilistic analysis of three-player symmetric quantum games played using the Einstein–Podolsky–Rosen–Bohm setting. Phys. Lett. A 372, 6564 (2008)MathSciNetCrossRefADSMATH
11.
Zurück zum Zitat Flitney, A.P., Abbott, D.: Quantum version of the Monty Hall problem. Phys. Rev. A 65, 062318 (2002)CrossRefADS Flitney, A.P., Abbott, D.: Quantum version of the Monty Hall problem. Phys. Rev. A 65, 062318 (2002)CrossRefADS
12.
Zurück zum Zitat Iqbal, A., Toor, A.H.: Quantum mechanics gives stability to Nash equilibrium. Phys. Rev. A 65, 022036 (2002)MathSciNet Iqbal, A., Toor, A.H.: Quantum mechanics gives stability to Nash equilibrium. Phys. Rev. A 65, 022036 (2002)MathSciNet
14.
18.
Zurück zum Zitat DAriano, G.M., Gill, R.D., Keyl, M., Kuemmerer, B., Maassen, H., Werner, R.F.: The quantum Monty Hall problem. Quant. Inf. Comp. 2, 355 (2002)MathSciNetMATH DAriano, G.M., Gill, R.D., Keyl, M., Kuemmerer, B., Maassen, H., Werner, R.F.: The quantum Monty Hall problem. Quant. Inf. Comp. 2, 355 (2002)MathSciNetMATH
19.
20.
Zurück zum Zitat Puya, S., Hoshang, H.: Quantum solution to a three player Kolkata restaurant problem using entangled qutrits. arXiv:1111.1962 [quant-ph], (2011) Puya, S., Hoshang, H.: Quantum solution to a three player Kolkata restaurant problem using entangled qutrits. arXiv:​1111.​1962 [quant-ph], (2011)
21.
Zurück zum Zitat Chakrabarti, A.S., Chakrabarti, B.K., Chatterjee, A., Mitra, M.: The Kolkata paise restaurant problem and resource utilization. Phys. A 388, 2420–2426 (2009)CrossRef Chakrabarti, A.S., Chakrabarti, B.K., Chatterjee, A., Mitra, M.: The Kolkata paise restaurant problem and resource utilization. Phys. A 388, 2420–2426 (2009)CrossRef
22.
Zurück zum Zitat Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301(R) (2001)CrossRefADS Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301(R) (2001)CrossRefADS
23.
24.
Zurück zum Zitat Flitney, A.P., Greentree, A.D.: Coalitions in the quantum Minority game: classical cheats and quantum bullies. Phys. Lett. A 362, 132 (2007)CrossRefADSMATH Flitney, A.P., Greentree, A.D.: Coalitions in the quantum Minority game: classical cheats and quantum bullies. Phys. Lett. A 362, 132 (2007)CrossRefADSMATH
25.
26.
Zurück zum Zitat Flitney, A.P., Hollenberg, L.C.L.: Multiplayer quantum minority game with decoherence. Quantum Inf. Comput. 7, 111 (2007)MathSciNetMATH Flitney, A.P., Hollenberg, L.C.L.: Multiplayer quantum minority game with decoherence. Quantum Inf. Comput. 7, 111 (2007)MathSciNetMATH
29.
Zurück zum Zitat Khan, S., Ramzan, M., Khan, M.K.: Quantum Monty Hall problem under decoherence. Commun. Theor. Phys. 54, 47 (2010)CrossRefADSMATH Khan, S., Ramzan, M., Khan, M.K.: Quantum Monty Hall problem under decoherence. Commun. Theor. Phys. 54, 47 (2010)CrossRefADSMATH
30.
Zurück zum Zitat Gawron, P., Miszczak, J.A., Sladkowski, J.: Noise effects in quantum magic squares game. Int. J. Quant. Inf. 6, 667 (2008)CrossRefMATH Gawron, P., Miszczak, J.A., Sladkowski, J.: Noise effects in quantum magic squares game. Int. J. Quant. Inf. 6, 667 (2008)CrossRefMATH
32.
Zurück zum Zitat Chen, L.K., Ang, H., Kiang, D., Kwek, L.C., Lo, C.F.: Quantum prisoner dilemma under decoherence. Phys. Lett. A 316, 317 (2003)CrossRefADSMATH Chen, L.K., Ang, H., Kiang, D., Kwek, L.C., Lo, C.F.: Quantum prisoner dilemma under decoherence. Phys. Lett. A 316, 317 (2003)CrossRefADSMATH
33.
Zurück zum Zitat Zhu, X., Kuang, L.M.: The influence of entanglement and decoherence on the quantum Stackelberg duopoly game. J. Phys. A Math. Theor. 40, 7729 (2007)MathSciNetCrossRefADSMATH Zhu, X., Kuang, L.M.: The influence of entanglement and decoherence on the quantum Stackelberg duopoly game. J. Phys. A Math. Theor. 40, 7729 (2007)MathSciNetCrossRefADSMATH
34.
36.
Zurück zum Zitat Khan, S., Ramzan, M., Khan, M.K.: Decoherence effects on multiplayer cooperative quantum games. Commun. Theor. Phys. 56, 228–234 (2011)CrossRefMATH Khan, S., Ramzan, M., Khan, M.K.: Decoherence effects on multiplayer cooperative quantum games. Commun. Theor. Phys. 56, 228–234 (2011)CrossRefMATH
37.
Zurück zum Zitat Gawron, P., Kurzyk, D., Pawela, L.: Decoherence effects in the quantum qubit flip game using Markovian approximation. Quantum. Inf. Process. 13, 665–682 (2014)MathSciNetCrossRefMATH Gawron, P., Kurzyk, D., Pawela, L.: Decoherence effects in the quantum qubit flip game using Markovian approximation. Quantum. Inf. Process. 13, 665–682 (2014)MathSciNetCrossRefMATH
38.
Zurück zum Zitat Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988)CrossRefADS Aharonov, Y., Albert, D.Z., Vaidman, L.: How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351 (1988)CrossRefADS
39.
Zurück zum Zitat Aharonov, Y., Botero, A., Pospescu, S., Reznik, B., Tollaksen, J.: Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values. Phys. Lett. A 301, 130 (2002)MathSciNetCrossRefADSMATH Aharonov, Y., Botero, A., Pospescu, S., Reznik, B., Tollaksen, J.: Revisiting Hardy’s paradox: counterfactual statements, real measurements, entanglement and weak values. Phys. Lett. A 301, 130 (2002)MathSciNetCrossRefADSMATH
40.
Zurück zum Zitat Lundeen, J.S., Steinberg, A.M.: Experimental joint weak measurement on a photon pair as a probe of Hardys paradox. Phys. Rev. Lett. 102, 020404 (2009)CrossRefADS Lundeen, J.S., Steinberg, A.M.: Experimental joint weak measurement on a photon pair as a probe of Hardys paradox. Phys. Rev. Lett. 102, 020404 (2009)CrossRefADS
41.
Zurück zum Zitat Yokota, K., Yamamoto, T., Koashi, M., Imoto, N.: Direct observation of Hardy’s paradox by joint weak measurement with an entangled photon pair. N. J. Phys. 11, 033011 (2009)CrossRef Yokota, K., Yamamoto, T., Koashi, M., Imoto, N.: Direct observation of Hardy’s paradox by joint weak measurement with an entangled photon pair. N. J. Phys. 11, 033011 (2009)CrossRef
42.
Zurück zum Zitat Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)CrossRefADS Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)CrossRefADS
43.
Zurück zum Zitat Kim, Y.S., Cho, Y.W., Ra, Y.S., Kim, Y.H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)CrossRefADS Kim, Y.S., Cho, Y.W., Ra, Y.S., Kim, Y.H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)CrossRefADS
44.
Zurück zum Zitat Lee, J.C., Jeong, Y.C., Kim, Y.S., Kim, Y.H.: Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 16309 (2011)CrossRefADS Lee, J.C., Jeong, Y.C., Kim, Y.S., Kim, Y.H.: Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 16309 (2011)CrossRefADS
45.
Zurück zum Zitat Kim, Y.S., Lee, J.C., Kwon, O., Kim, Y.H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117 (2012)CrossRef Kim, Y.S., Lee, J.C., Kwon, O., Kim, Y.H.: Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117 (2012)CrossRef
46.
Zurück zum Zitat Man, Z.X., Xia, Y.J., An, N.B.: Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements. Phys. Rev. A 86, 052322 (2012)CrossRefADS Man, Z.X., Xia, Y.J., An, N.B.: Enhancing entanglement of two qubits undergoing independent decoherences by local pre- and postmeasurements. Phys. Rev. A 86, 052322 (2012)CrossRefADS
47.
Zurück zum Zitat Burger, E., Freund, J.E.: Introduction to the Theory of Games. Prentice-Hall, Englewood Cliffs (1963) Burger, E., Freund, J.E.: Introduction to the Theory of Games. Prentice-Hall, Englewood Cliffs (1963)
48.
Zurück zum Zitat Wang, S.C., Yu, Z.W., Zou, W.J., Wang, X.B.: Protecting quantum states from decoherence of finite temperature using weak measurement. Phys. Rev. A 89, 022318 (2014)CrossRefADS Wang, S.C., Yu, Z.W., Zou, W.J., Wang, X.B.: Protecting quantum states from decoherence of finite temperature using weak measurement. Phys. Rev. A 89, 022318 (2014)CrossRefADS
49.
Zurück zum Zitat Du, J., Li, H., Xu, X., Shi, M., Wu, J., Zhou, X., Han, R.: Experimental realization of quantum games on a quantum computer. Phys. Rev. Lett. 88, 137902 (2002)CrossRefADS Du, J., Li, H., Xu, X., Shi, M., Wu, J., Zhou, X., Han, R.: Experimental realization of quantum games on a quantum computer. Phys. Rev. Lett. 88, 137902 (2002)CrossRefADS
50.
Zurück zum Zitat Prevedel, R., Stefanov, A., Walther, P., Zeilinger, A.: Experimental realization of a quantum game on a one-way quantum computer. N. J. Phys. 9, 205 (2007)CrossRef Prevedel, R., Stefanov, A., Walther, P., Zeilinger, A.: Experimental realization of a quantum game on a one-way quantum computer. N. J. Phys. 9, 205 (2007)CrossRef
51.
Zurück zum Zitat Kolenderski, P., Sinha, U., Youning, L., Zhao, T., Volpini, M., Cabello, A., Laflamme, R., Jennewein, T.: Aharon–Vaidman quantum game with a Young-type photonic qutrit. Phys. Rev. A 86, 012321 (2012)CrossRefADS Kolenderski, P., Sinha, U., Youning, L., Zhao, T., Volpini, M., Cabello, A., Laflamme, R., Jennewein, T.: Aharon–Vaidman quantum game with a Young-type photonic qutrit. Phys. Rev. A 86, 012321 (2012)CrossRefADS
52.
Zurück zum Zitat Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)CrossRefADS Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)CrossRefADS
53.
Zurück zum Zitat Katz, N., Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., OConnell, A., Wang, H., Cleland, A.N., Martinis, J.M., Korotkov, A.N.: Reversal of the weak measurement of a quantum state in a superconducting phase qubit. Phys. Rev. Lett. 101, 200401 (2008)CrossRefADS Katz, N., Neeley, M., Ansmann, M., Bialczak, R.C., Hofheinz, M., Lucero, E., OConnell, A., Wang, H., Cleland, A.N., Martinis, J.M., Korotkov, A.N.: Reversal of the weak measurement of a quantum state in a superconducting phase qubit. Phys. Rev. Lett. 101, 200401 (2008)CrossRefADS
54.
Zurück zum Zitat Kim, Y.S., Cho, Y.W., Ra, Y.S., Kim, Y.H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)CrossRefADS Kim, Y.S., Cho, Y.W., Ra, Y.S., Kim, Y.H.: Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978 (2009)CrossRefADS
Metadaten
Titel
Improving the payoffs of cooperators in three-player cooperative game using weak measurements
verfasst von
Xiang-Ping Liao
Xiang-Zhuo Ding
Mao-Fa Fang
Publikationsdatum
01.12.2015
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 12/2015
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-015-1144-4

Weitere Artikel der Ausgabe 12/2015

Quantum Information Processing 12/2015 Zur Ausgabe