Generalized Quantum Games with Nash Equilibrium
Generalized Quantum Games with Nash Equilibrium
摘要
We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it.The scheme is implemented with a single spin qubit system and a two-entangled-qubit system.The Nash Equilibrium Theorem is proved for the models.
基金
国家自然科学基金,国家重点基础研究发展计划(973计划)
参考文献12
-
1[1]For a review see,e.g.,C.H.Bennett and D.P.DiVincenzo,Nature 404(2000)247;M.A.Nielsen and I.L.Chuang,Quantum Computation and Quantum Information,Cambridge University Press,Cambridge(2000).
-
2[2]D.A.Meyer,Phys.Rev.Lett.82(1999)1052.
-
3[3]J.Eisert,M.Wilkens,and M.Lewenstein,Phys.Rev.Lett.83(1999)3077.
-
4[4]L.Goldenberg,L.Vaidman,and S.Wiesner,Phys.Rev.Lett.82(1999)3356;S.C.Benjamin and P.M.Hayden,Phys.Rev.A64(2001)030301;N.F.Johnson,Phys.Rev.A63(2001)020302.
-
5[5]J.Du,H.Li,X.Xu,M.Shi,J.Wu,X.Zhou,and R.Han,Phys.Rev.Lett.88(2002)137902.
-
6[6]J.von Neumann and O.Morgenstern,The Theory of Games and Economic Behaviour,Princeton University Press,Princeton,NJ(1947);For an introduction,see,e.g.,E.Rasmusen,Games and Information,Blackwell,Oxford,UK(1995).
-
7[7]A.Einstein,B.Podolsky,and N.Rosen,Phys.Rev.47(1935)77.
-
8[8]J.F.Nash,Adv.Math.54(1951)286.
-
9[9]C.F.Lee and N.Johnson,Quantum Game Theory,LANL e-print,Quant-ph/0207012.
-
10[10]C.P.Sun,Phys.Rev.A48(1993)878;C.P.Sun,et al.,Fortschr.Phys.43(1995)585.
-
1CHENBo,MAYing-Jun,LONGGui-Lu.Quantum Game with Restricted Matrix Strategies[J].Communications in Theoretical Physics,2003,40(6X):655-658.
-
2A.Iqbal A.H.Toor.Stability of Mixed Nash Equilibria in Symmetric Quantum Games[J].Communications in Theoretical Physics,2004,42(3X):335-338.
-
3郭晓春,张大林.非合作博弈中的正则平衡点[J].西南民族大学学报(自然科学版),2012,38(6):896-898.
-
4ZHAOHai-Jun FANGXi-Ming.Influence of Constraint in Parameter Space on Quantum Games[J].Communications in Theoretical Physics,2004,41(4):541-546.
-
5Salman Khan,M.Ramzan,M.Khalid.Khan.Decoherence Effects on Multiplayer Cooperative Quantum Games[J].Communications in Theoretical Physics,2011,56(8):228-234.
-
6嵇英华,蔡十华,乐建新,王资生.Operating a geometric quantum gate by external controllable parameters[J].Chinese Physics B,2010,19(1):84-89. 被引量:1
-
7李威,赵红敏,林家逖.量子博弈论及其应用[J].大学物理,2003,22(12):3-8. 被引量:5
-
8先进核磁共振系统落户合肥[J].合肥科技,2006(6):13-13.
-
9孙世军,黄永莲,赵鹏飞.核磁共振系统产生A-A相时的量子跃迁[J].湛江师范学院学报,2002,23(3):11-16.
-
10邱正明,康士秀,霍剑青.用核磁共振系统测交流磁场的实验方法[J].国际物理教育通讯,2006(2):40-42.