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).

FullText HTML : translate this paragraph

References

[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

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

[1]	Huang Tian-Long, Wu Yong-Zheng, Ni Ming, Wang Shi, Ye Yong-Jin. Effects of quantum noise on Shor’s algorithm. Acta Physica Sinica, 2024, 73(5): 050301. doi: 10.7498/aps.73.20231414
[2]	Wu Yu-Kai, Duan Lu-Ming. Research progress of ion trap quantum computing. Acta Physica Sinica, 2023, 72(23): 230302. doi: 10.7498/aps.72.20231128
[3]	Fan Heng. Breakthrough of error correction in quantum computing. Acta Physica Sinica, 2023, 72(7): 070303. doi: 10.7498/aps.72.20230330
[4]	Jiang Da, Yu Dong-Yang, Zheng Zhan, Cao Xiao-Chao, Lin Qiang, Liu Wu-Ming. Research progress of material, physics, and device of topological superconductors for quantum computing. Acta Physica Sinica, 2022, 71(16): 160302. doi: 10.7498/aps.71.20220596
[5]	Wang Mei-Hong, Hao Shu-Hong, Qin Zhong-Zhong, Su Xiao-Long. Research advances in continuous-variable quantum computation and quantum error correction. Acta Physica Sinica, 2022, 71(16): 160305. doi: 10.7498/aps.71.20220635
[6]	Wang Chen-Xu, He Ran, Li Rui-Rui, Chen Yan, Fang Ding, Cui Jin-Ming, Huang Yun-Feng, Li Chuan-Feng, Guo Guang-Can. Advances in the study of ion trap structures in quantum computation and simulation. Acta Physica Sinica, 2022, 71(13): 133701. doi: 10.7498/aps.71.20220224
[7]	Zhou Zong-Quan. “Quantum memory” quantum computers and noiseless phton echoes. Acta Physica Sinica, 2022, 71(7): 070305. doi: 10.7498/aps.71.20212245
[8]	Wang Ning, Wang Bao-Chuan, Guo Guo-Ping. New progress of silicon-based semiconductor quantum computation. Acta Physica Sinica, 2022, 71(23): 230301. doi: 10.7498/aps.71.20221900
[9]	Zhang Jie-Yin, Gao Fei, Zhang Jian-Jun. Research progress of silicon and germanium quantum computing materials. Acta Physica Sinica, 2021, 70(21): 217802. doi: 10.7498/aps.70.20211492
[10]	Zhang Shi-Hao, Zhang Xiang-Dong, Li Lü-Zhou. Research progress of measurement-based quantum computation. Acta Physica Sinica, 2021, 70(21): 210301. doi: 10.7498/aps.70.20210923
[11]	Chen Ran-Yi-Liu, Zhao Ben-Chi, Song Zhi-Xin, Zhao Xuan-Qiang, Wang Kun, Wang Xin. Hybrid quantum-classical algorithms: Foundation, design and applications. Acta Physica Sinica, 2021, 70(21): 210302. doi: 10.7498/aps.70.20210985
[12]	He Ying-Ping, Hong Jian-Song, Liu Xiong-Jun. Non-abelian statistics of Majorana modes and the applications to topological quantum computation. Acta Physica Sinica, 2020, 69(11): 110302. doi: 10.7498/aps.69.20200812
[13]	Tian Yu-Ling, Feng Tian-Feng, Zhou Xiao-Qi. Collaborative quantum computation with redundant graph state. Acta Physica Sinica, 2019, 68(11): 110302. doi: 10.7498/aps.68.20190142
[14]	Fan Heng. Quantum computation and quantum simulation. Acta Physica Sinica, 2018, 67(12): 120301. doi: 10.7498/aps.67.20180710
[15]	Zhao Shi-Ping, Liu Yu-Xi, Zheng Dong-Ning. Novel superconducting qubits and quantum physics. Acta Physica Sinica, 2018, 67(22): 228501. doi: 10.7498/aps.67.20180845
[16]	Zhao Na, Liu Jian-She, Li Tie-Fu, Chen Wei. Progress of coupled superconducting qubits. Acta Physica Sinica, 2013, 62(1): 010301. doi: 10.7498/aps.62.010301
[17]	Li Pan-Chi, Wang Hai-Ying, Song Kao-Ping, Yang Er-Long. Research on the improvement of quantum potential well-based particle swarm optimization algorithm. Acta Physica Sinica, 2012, 61(6): 060302. doi: 10.7498/aps.61.060302
[18]	Yao Xi-Wei, Zeng Bi-Rong, Liu Qin, Mu Xiao-Yang, Lin Xing-Cheng, Yang Chun, Pan Jian, Chen Zhong. Subspace quantum process tomography via nuclear magnetic resonance. Acta Physica Sinica, 2010, 59(10): 6837-6841. doi: 10.7498/aps.59.6837
[19]	Ye Bin, Xu Wen-Bo, Gu Bin-Jie. Robust quantum computation of the quantum kicked Harper model and dissipative decoherence. Acta Physica Sinica, 2008, 57(2): 689-695. doi: 10.7498/aps.57.689
[20]	Ye Bin, Gu Rui-Jun, Xu Wen-Bo. Robust quantum computation of the kicked Harper model and quantum chaos. Acta Physica Sinica, 2007, 56(7): 3709-3718. doi: 10.7498/aps.56.3709

Catalog

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

Metrics

Abstract views: 3313
PDF Downloads: 88
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板