Optimal asymmetric phase-covariant quantum cloning

We propose a relatively simple method to derive the optimal asymmetric approximate quantum cloning. The results obtained agree with the previous contributions. Utilizing the method we also obtain the optimal asymmetric 1→3 phase-covariant quantum cloning and 1→2 and 1→3 economical ones, which work without ancilla, in 2-dimension. Maybe the method can be effective to derive the optimal asymmetric approximate N→M quantum cloning in d-dimension.