About economic qubit cloning

In this paper we establish a deep connection between the 3 qubit one-to-two phase-covariant quantum cloning network of Fuchs et al. [C. Fuchs, N. Gisin, R.B. Griffiths, C.S. Niu, and A. Peres, Phys. Rev. A 56 no 4, 1163 (1997)], and its economic 2 qubit counterpart due to Niu and Griffiths [Phys.Rev. A 60 no 4, 2764 (1999)]. A general, necessary and sufficient criterion is derived in order to characterize the reducibility of 3 qubit cloners to 2 qubit cloners. When this criterion is fulfilled, economic cloning is possible. We show that the optimal isotropic or universal 3 qubit cloning machine is not reducible to a 2 qubit cloner.