Optimal cloning of pure states, testing single clones

We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state σ into MN systems of the same kind, in an approximation of the M-fold tensor product of the state σ. In a previous paper it was shown that this problem has a unique optimal solution, when the quality of the output is judged by arbitrary measurements, involving also the correlations between the clones. We show in this paper, that if the quality judgment is based solely on measurements of single output clones, there is again a unique optimal cloning device, which coincides with the one found previously.