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

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• 作者：Xiang-Ping Liao ; Xiang-Zhuo Ding ; Mao-Fa Fang
• 关键词：Three ; player cooperative game ; Decoherence ; The payoff ; Weak measurement
• 刊名：Quantum Information Processing
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：14
• 期：12
• 页码：4395-4412
• 全文大小：1,599 KB
• 参考文献：1.von-Neumann, J., Morgenstein, O.: The Theory of Games and Economic Behaviour. Princeton University Press, Princeton, NJ (1944)
  2.Nash, J.: Equilibrium points in n-person games. Proc. Nat. Acad. Sci. 36, 48 (1950)MathSciNet CrossRef ADS
  3.Meyer, D.A.: Quantum strategies. Phys. Rev. Lett. 82, 1052 (1999)MathSciNet CrossRef ADS
  4.Eisert, J., Wilkens, M., Lewenstein, M.: Quantum games and quantum strategies. Phy. Rev. Lett. 83, 3077 (1999)MathSciNet CrossRef ADS
  5.Marinatto, L., Weber, T.: A quantum approach to static games of complete information. Phys. Lett. A 272, 291 (2000)MathSciNet CrossRef ADS
  6.Flitney, A.P., Abbott, D.: Quantum games with decoherence. J. Phys. A 38, 449 (2005)MathSciNet CrossRef ADS
  7.Cheon, T., Iqbal, A.: Bayesian Nash equilibria and Bell inequalities. J. Phys. Soc. Jpn. 77, 024801 (2008)CrossRef ADS
  8.Iqbal, A., Abbott, D.: Quantum matching pennies game. J. Phy. Soc. Jpn. 78, 014803 (2009)CrossRef ADS
  9.Iqbal, A., Cheon, T., Abbott, D.: Probabilistic analysis of three-player symmetric quantum games played using the Einstein鈥揚odolsky鈥揜osen鈥揃ohm setting. Phys. Lett. A 372, 6564 (2008)MathSciNet CrossRef ADS
  10.Iqbal, A., Toor, A.H.: Evolutionarily stable strategies in quantum games. Phys. Lett. A 280, 249 (2001)MathSciNet CrossRef ADS
  11.Flitney, A.P., Abbott, D.: Quantum version of the Monty Hall problem. Phys. Rev. A 65, 062318 (2002)CrossRef ADS
  12.Iqbal, A., Toor, A.H.: Quantum mechanics gives stability to Nash equilibrium. Phys. Rev. A 65, 022036 (2002)MathSciNet
  13.Eisert, J., Wilkens, M.: Quantum games. J. Mod. Opt. 47, 2543 (2000)MathSciNet CrossRef ADS
  14.Ramzan, M., Khan, M.K.: Noise effects in a three-player Prisoner鈥檚 dilemma quantum game. J. Phys. A Math. Theor. 41, 435302 (2008)MathSciNet CrossRef ADS
  15.Flitney, A.P., Ng, J., Abbott, D.: Quantum Parrondo鈥檚 games. Phys. A 314, 35 (2002)MathSciNet CrossRef
  16.Iqbal, A., Toor, A.H.: Quantum cooperative games. Phys. Lett. A 293, 103 (2002)MathSciNet CrossRef ADS
  17.Johnson, N.F.: Playing a quantum game with a corrupted source. Phys. Rev. A 63, 020302(R) (2001)CrossRef ADS
  18.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)
  19.Miszczak, J.A., Gawron, P., Puchala, Z.: Qubit flip game on a Heisenberg spin chain. arXiv:鈥?108.鈥?642 [quant-ph], (2011)
  20.Puya, S., Hoshang, H.: Quantum solution to a three player Kolkata restaurant problem using entangled qutrits. arXiv:鈥?111.鈥?962 [quant-ph], (2011)
  21.Chakrabarti, A.S., Chakrabarti, B.K., Chatterjee, A., Mitra, M.: The Kolkata paise restaurant problem and resource utilization. Phys. A 388, 2420鈥?426 (2009)CrossRef
  22.Benjamin, S.C., Hayden, P.M.: Multiplayer quantum games. Phys. Rev. A 64, 030301(R) (2001)CrossRef ADS
  23.Chen, Q., Wang, Y.: N-player quantum minority game. Phys. Lett. A A 327, 98,102 (2004)
  24.Flitney, A.P., Greentree, A.D.: Coalitions in the quantum Minority game: classical cheats and quantum bullies. Phys. Lett. A 362, 132 (2007)CrossRef ADS
  25.Schmid, C., Flitney, A.P.: Experimental implementation of a four-player quantum game. arXiv:鈥?901.鈥?063v1 [quant-ph], (2008)
  26.Flitney, A.P., Hollenberg, L.C.L.: Multiplayer quantum minority game with decoherence. Quantum Inf. Comput. 7, 111 (2007)MathSciNet
  27.Flitney, A.P., Abbott, D.: Quantum games with decoherence. J. Phys. A Math. Gen. 38, 449 (2005)MathSciNet CrossRef ADS
  28.Khan, S., Ramzan, M., Khan, M.K.: Quantum Parrondos games under decoherence. Int. J. Theor. Phys 49, 31 (2010)MathSciNet CrossRef
  29.Khan, S., Ramzan, M., Khan, M.K.: Quantum Monty Hall problem under decoherence. Commun. Theor. Phys. 54, 47 (2010)CrossRef ADS
  30.Gawron, P., Miszczak, J.A., Sladkowski, J.: Noise effects in quantum magic squares game. Int. J. Quant. Inf. 6, 667 (2008)CrossRef
  31.Gawron, P.: Noisy quantum Monty Hall game. Fluct. Noise Lett. 9, 9 (2010)MathSciNet CrossRef
  32.Chen, L.K., Ang, H., Kiang, D., Kwek, L.C., Lo, C.F.: Quantum prisoner dilemma under decoherence. Phys. Lett. A 316, 317 (2003)CrossRef ADS
  33.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)MathSciNet CrossRef ADS
  34.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)MathSciNet CrossRef ADS
  35.Ramzan, M.: Three-player quantum Kolkata restaurant problem under decoherence. Quantum Inf. Process. 12(1), 577鈥?86 (2013)MathSciNet CrossRef ADS
  36.Khan, S., Ramzan, M., Khan, M.K.: Decoherence effects on multiplayer cooperative quantum games. Commun. Theor. Phys. 56, 228鈥?34 (2011)CrossRef
  37.Gawron, P., Kurzyk, D., Pawela, L.: Decoherence effects in the quantum qubit flip game using Markovian approximation. Quantum. Inf. Process. 13, 665鈥?82 (2014)MathSciNet CrossRef
  38.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)CrossRef ADS
  39.Aharonov, Y., Botero, A., Pospescu, S., Reznik, B., Tollaksen, J.: Revisiting Hardy鈥檚 paradox: counterfactual statements, real measurements, entanglement and weak values. Phys. Lett. A 301, 130 (2002)MathSciNet CrossRef ADS
  40.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)CrossRef ADS
  41.Yokota, K., Yamamoto, T., Koashi, M., Imoto, N.: Direct observation of Hardy鈥檚 paradox by joint weak measurement with an entangled photon pair. N. J. Phys. 11, 033011 (2009)CrossRef
  42.Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)CrossRef ADS
  43.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)CrossRef ADS
  44.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)CrossRef ADS
  45.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.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)CrossRef ADS
  47.Burger, E., Freund, J.E.: Introduction to the Theory of Games. Prentice-Hall, Englewood Cliffs (1963)
  48.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)CrossRef ADS
  49.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)CrossRef ADS
  50.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.Kolenderski, P., Sinha, U., Youning, L., Zhao, T., Volpini, M., Cabello, A., Laflamme, R., Jennewein, T.: Aharon鈥揤aidman quantum game with a Young-type photonic qutrit. Phys. Rev. A 86, 012321 (2012)CrossRef ADS
  52.Korotkov, A.N., Jordan, A.N.: Undoing a weak quantum measurement of a solid-state qubit. Phys. Rev. Lett. 97, 166805 (2006)CrossRef ADS
  53.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)CrossRef ADS
  54.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)CrossRef ADS
  
• 作者单位：Xiang-Ping Liao (1)
  Xiang-Zhuo Ding (2)
  Mao-Fa Fang (3)
  
  1. College of Science, Hunan University of Technology, Zhuzhou, 412008, Hunan, China
  2. College of Mechanical and Vehicle Engineering, Hunan University, Changsha, 410081, Hunan, China
  3. College of Physics and Information Science, Hunan Normal University, Changsha, 410081, Hunan, China
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Mathematics
  Engineering, general
  Computer Science, general
  Characterization and Evaluation Materials
  
• 出版者：Springer Netherlands
• ISSN：1573-1332

文摘

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. Keywords Three-player cooperative game Decoherence The payoff Weak measurement