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Phase-covariant quantum cloning

We consider an N -> M quantum cloning transformation acting on pure two-level states lying on the equator of the Bloch sphere. An upper bound for its fidelity is presented, by establishing a connection between optimal phase covariant cloning and phase estimation. We give the explicit form of a cloning transformation that achieves the bound for the case N=1, M=2, and find a link between this case and optimal eavesdropping in the quantum cryptographic scheme BB84.