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Constructing Entanglers in 2-Players–N-Strategies Quantum Game

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DOI: 10.4236/jqis.2015.51003    2,622 Downloads   2,973 Views   Citations
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In quantum games based on 2-player-N-strategies classical games, each player has a quNit (a normalized vector in an N-dimensional Hilbert space HN) upon which he applies his strategy (a matrix USU(N)). The players draw their payoffs from a state . Here  and J (both determined by the game’s referee) are respectively an unentangled 2-quNit (pure) state and a unitary operator such that  is partially entangled. The existence of pure strategy Nash equilibrium in the quantum game is intimately related to the degree of entanglement of . Hence, it is practical to design the entangler J= J(β) to be dependent on a single real parameter β that controls the degree of entanglement of , such that its von-Neumann entropy SN(β) is continuous and obtains any value in . Designing J(β) for N=2 is quite standard. Extension to N>2 is not obvious, and here we suggest an algorithm to achieve it. Such construction provides a special quantum gate that should be a useful tool not only in quantum games but, more generally, as a special gate in manipulating quantum information protocols.

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The authors declare no conflicts of interest.

Cite this paper

Avishai, Y. (2015) Constructing Entanglers in 2-Players–N-Strategies Quantum Game. Journal of Quantum Information Science, 5, 16-23. doi: 10.4236/jqis.2015.51003.


[1] Nielsen, M.A. and Chuang, I.L. (2000) Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, p 26, Fig. 1.13.
[2] Band, Y.B. and Avishai, Y. (2013) Quantum Mechanics with Application to Nanotechnology and Information Science. Academic Press, Waltham, p 217.
[3] Goldenberg, L., Vaidman, L. and Wiesner, S. (1999) Quantum Gambling. Physical Review Letters, 82, 3356.
[4] Meyer, D. (1999) Quantum Strategies. Physical Review Letters, 82, 1052-1055.
[5] Eisert, J., Wilkens, M. and Lewenstein, M. (1999) Quantum Games and Quantum Strategies. Physical Review Letters, 83, 3077-3080.
[6] Flitney, A.P. and Abbott, D. (2002) An Introduction to Quantum Game Theory. Fluctuation and Noise Letters, 2, R175-R187. arXiv: quant-ph/0208069.
[7] Piotrowski, E.W. andSlaadkowski, J. (2003) An Invitation to Quantum Game Theory. International Journal of Theoretical Physics, 42, 1089-1099.
[8] Landsburg, S.E. (2004) Quantum Game Theory. Notices of the American Mathematical Society, 51, 394-399.
[9] Iqbal, A. (2004) Studies in the Theory of Quantum Games. Ph.D thesis, Quaid-i-Azam University, Islamabad, 137 p. arXiv:quant-phys/050317.
[10] Sharif, P. and Heydari, H. (2014) Quantum Information and Computation, 14, 0295.
[11] Landsburg, S.E. (2011) Nash Equilibria in Quantum Games. Proceedings of the American Mathematical Society, 139, 4423-4434. arXiv:1110.1351.
[12] Benjamin, S.C. and Hayden, P.M. (2001) Comment on “Quantum Games and Quantum Strategies”. Physical Review Letters, 87, Article ID: 069801.
[13] Du, J., Li, H., Xu, X., Han, R. and Zhou, X. (2002) Entanglement Enhanced Multiplayer Quantum Games. Physics Letters A, 302, 229-233.
[14] Du, J., Xu, X., Li, H., Zhou, X. and Han, R. (2002) Playing Prisoner’s Dilemma with Quantum Rules. Fluctuation and Noise Letters, 2, R189.
[15] Flitney, A.P. and Abbott, D. (2003) Advantage of a Quantum Player over a Classical One in 2 × 2 Quantum Games. Proceedings of the Royal Society A, 459, 2463-2474.
[16] Flitney, A.P. and Hollenberg, L.C.L. (2007) Nash Equilibria in Quantum Games with Generalized Two-Parameter Strategies. Physics Letters A, 363, 381-388.
[17] Avishai, Y. (2012) Some Topics in Quantum Games. MA Thesis in Economics, Ben Gurion University, Beersheba, 96 p. arXiv:1306.0284. (Submitted on August 2012 to the Faculty of Social Science and Humanities at the Ben Gurion University).
[18] Osborne, M.J. and Rubinstein, A. (2011) A Course in Game Theory. The MIT Press, Version: 2011-1-19. Cambridge, Massachusetts, London, England.

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