  Assuming the condition of no superluminal signalling, we got an upper bound
on the quality of all asymmetric $ 1\to 2$ cloning machines, acting on qubits
whose Bloch vectors lie on a great circle. Then we constructed an $ 1\to 2$
cloning machine, which asymmetrically clone all qubits corresponding to this
great circle, and this machine matches with that upper bound, and hence this is
optimal one.
