We consider an →NM 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.
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Bruß et al. (2000) studied this question.