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Cambridge University Press, Cambridge, U.K.
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For an overview, see M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, U.K., 2000). Quantum computation is discussed in Chap., and the role of the controlled-NOT operation as a universal gate is discussed in Sec. 4.5.
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Note that the relevance of this exchange of roles between the target and control qubit for specific quantum-computational problems, in particular for the Bernstein-Vazirani problem, has been pointed out by N. D. Mermin (unpublished).
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Mermin, N.D.1
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R. F. Werner, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.40.4277 40, 4277 (1989).
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In fact, the type of noise represented by Eq. 8 is indeed equivalent to the kind of noise against which the entanglement capability of the gate is least robust, as derived by A. W. Harrow and M. A. Nielsen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.012308 68, 012308 (2003). The arguments given in that paper therefore provide a formal proof that this noise model is optimal for estimating the minimal entanglement capability of the gate.
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See, for example, H. F. Hofmann and S. Takeuchi, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.68.032103 68, 032103 (2003);
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