Phase-covariant quantum cloning

We consider an $\overrightarrow{N}M$ 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.