Quantum game— “PQ” problem

Yang Xiao-Kun; Li Wei; Huang Yong-Chang

doi:10.7498/aps.73.20230592

Abstract

This paper reviews the coin flipping problem of “PQ” in a classical two-player game, and shows that when one player adopts quantum strategy, he can beat his classical opponent and gain higher returns. By using quantitative means, the whole “PQ” problem is put under a more general and fair condition, and it is generalized and studied again from many aspects and angles. Finally, we obtain some more essential and important conclusions, and explain the conclusions and its practical significance through some practical examples. At the same time, this paper gives the definition of imperfect fair game and the definition of perfect fair game, revises the quantum coin flipping game to make the game fair, and studies a multi-round version of quantum coin flipping. Some basic conclusions of fair quantum game are obtained, and the meaning of perfectly fair game is explained in practice.

Keywords:

Authors and contacts

Institute of Theoretical Physics, Beijing University of Technology, Beijing 100022, China

Corresponding author: Yang Xiao-Kun, xkyang1003@hotmail.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11875081).

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References

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Cited By

[1]	Nielsen M A Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) p306
[2]	Rasmusen E 2000 An Introduction to Game Theory (New Jersey: Blackwell Publishing) p19
[3]	Cheong K H, Koh J M, Jones M C 2019 BioEssays 41 1900027 Google Scholar
[4]	Koh J M, Cheong K H 2020 Adv. Sci. 7 2001126 Google Scholar
[5]	Cheong K H, Wen T, Lai J W 2020 Adv. Sci. 7 2002324 Google Scholar
[6]	Eisert J, Wilkens M, Lewensetein M 1999 Phys. Rev. Lett. 83 3077 Google Scholar
[7]	Benjamin S C, Hayden P M 2001 Phys. Rev. A 64 030301 Google Scholar
[8]	Rajendran J, Benjamin C 2018 R. Soc. Open Sci. 5 171599 Google Scholar
[9]	Rajendran J, Benjamin C 2018 Europhys. Lett. 122 40004 Google Scholar
[10]	Lai J W, Cheong K H 2020 Nonlinear Dyn. 100 849 Google Scholar
[11]	Lai J W, Cheong K H 2020 Phys. Rev. E 101 052212 Google Scholar
[12]	Lai J W, Tan J R A, Lu H, Yap Z R, Cheong K H 2020 Phys. Rev. E 102 012213 Google Scholar
[13]	Marinatto L, Weber T 2000 Phys. Lett. A272 291 Google Scholar
[14]	Du J F, Li H, Xu X D, Shi M J, Shi M, Wu J, Zhou X, Han R. 2002 Phys. Rev. Lett. 88 137902 Google Scholar
[15]	Meyer D A 1999 Phys. Rev. Lett. 82 1052 Google Scholar
[16]	Van Enk S J 2000 Phys. Rev. Lett. 84 789 Google Scholar
[17]	Meyer D A 2000 Phys. Rev. Lett. 84 790 Google Scholar
[18]	Huang Y C, Ma F C, Zhang N 2004 Mod. Phys. Lett. B18 1367 Google Scholar
[19]	Huang Y C, Liu M, Suo M 2007 Int. J. Mod. Phys. B21 4387 Google Scholar
[20]	Chang D, Huang Y C 2008 Mod. Phys. Lett. B 22 3145 Google Scholar
[21]	Huang Y C, Lee X G, Shao M X 2006 Mod. Phys. Lett. A21 1107 Google Scholar
[22]	Huang Y C, Yu C X 2007 Phys. Rev. D 75 044011 Google Scholar
[23]	Huang Y C, Huo Q H 2008 Phys. Lett. B 662 290 Google Scholar
[24]	Liao L, Huang Y C 2007 Ann. Phys. (N. Y.) 322 2469 Google Scholar
[25]	Fei S M, Gao X H, Wang X H, Wang Z X, Wu K 2003 Phys. Rev. A 68 022315 Google Scholar

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Vol. 73, Issue 3 - 2024-02-05

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