Probabilistically Perfect Cloning of Two Pure States: Geometric Approach.
We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary a priori probabilities. The solution emerges from a geometric formulation of the problem. This formulation reveals that cloning converges to state discrimination followed by state preparation as the number of clones goes to infinity. The convergence exhibits a phenomenon analogous to a second-order symmetry-breaking phase transition.
Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
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Yerokhin
Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
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Shehu
Department of Mathematics, Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016, USA.
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Feldman
Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.|Física Teòrica: Informació i Fenòmens Quàntics, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain.
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Bagan
Department of Physics and Astronomy, Hunter College of the City University of New York, 695 Park Avenue, New York, New York 10065, USA.
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Bergou