Economical phase-covariant cloning with multiclones

This paper presents a very simple method to derive the explicit transformations of the optimal economical 1 to M phase-covariant cloning. The fidelity of clones reaches the theoretic bound D'Ariano G M and Macchiavello C 2003 Phys. Rev. A 67 042306. The derived transformations cover the previous contributions Delgado Y, Lamata L et al, 2007 Phys. Rev. Lett. 98 150502 in which M must be odd.