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Mini-maximizing two qubit quantum computations

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Abstract

Two qubit quantum computations are viewed as two player, strictly competitive games and a game-theoretic measure of optimality of these computations is developed. To this end, the geometry of Hilbert space of quantum computations is used to establish the equivalence of game-theoretic solution concepts of Nash equilibrium and mini-max outcomes in games of this type, and quantum mechanisms are designed for realizing these mini-max outcomes.

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References

  1. Binmore, K.: Fun and Games. D.C. Heath, Lexington (1992)

  2. Bleiler, S.A.: A formalism for quantum games and an application, preprint arxiv:0808.1389v1 [quant-ph]. http://arxiv.org/abs/0808.1389

  3. Cortese, J.A.: Quantum Information Theory Classical Communication Over Quantum Channels. Doctoral Thesis, California Institute of Technology (2003)

  4. Grover, L.K.: A fast quantum mechanical algorithm for database search. In: Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (1996)

  5. Khan, F.S., Phoenix, S.J.D.: Gaming the quantum. Quantum Inf. Comput. 13(3 & 4), 231–244 (2013)

    Google Scholar 

  6. Khan, F.S., El Hady, A.: Gaming Quantum Neural Networks, presented at SPIE Defense, Security + Sensing (2013)

  7. Meyer, D.: Quantum games and quantum algorithms. In: Quantum Computation and Quantum Information Science, Contemporary Mathematics Series. American Mathematical Society (2002)

  8. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423, 623–656 (1948)

    Google Scholar 

  9. Schumacher, B.W., Westmoreland, M.: Optimal signal ensembles. Phys. Rev. A 63(2), 022308-1–022308-5 (2001)

    Google Scholar 

  10. Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Sci. Comput. 26(5), 1484–1509 (1997)

    Google Scholar 

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Authors and Affiliations

  1. Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, UAE

    Faisal Shah Khan

  2. Department of Electrical and Computer Engineering, Khalifa University, Abu Dhabi, UAE

    Simon J. D. Phoenix

Authors
  1. Faisal Shah Khan
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  2. Simon J. D. Phoenix
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Correspondence to Faisal Shah Khan.

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Khan, F.S., Phoenix, S.J.D. Mini-maximizing two qubit quantum computations. Quantum Inf Process 12, 3807–3819 (2013). https://doi.org/10.1007/s11128-013-0640-7

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  • DOI: https://doi.org/10.1007/s11128-013-0640-7

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