  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.
