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We consider quantum devices for turning a finite number N of d-level quantumsystems in the same unknown pure state \sigma into M>N systems of the samekind, in an approximation of the M-fold tensor product of the state \sigma. Ina previous paper it was shown that this problem has a unique optimal solution,when the quality of the output is judged by arbitrary measurements, involvingalso the correlations between the clones. We show in this paper, that if thequality judgement is based solely on measurements of single output clones,there is again a unique optimal cloning device, which coincides with the onefound previously.Comment: 16 Pages, REVTe

Optimal cloning of pure states, testing single clones