Probabilistically Perfect Cloning of Two Pure States: Geometric Approach
V. Yerokhin, Andi Shehu, É. P. Feľdman, E. Bagán, János A. Bergou · Physical Review Letters · 2016
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.