Quantum circuits for asymmetric 1 to n quantum cloning

In this paper, we considered asymmetric 1 → n cloning circuits generalized from the asymmetric 1 → 2 cloning circuit proposed by Bužek et al. [Phys. Rev. A 56, 3446 (1997)]. The generalization is based on an information flux insight of the original cloning circuit. Specifically, the circuit separately and sequentially transfers the Z-type information and X-type information of the input state to the output copies with controlled-not gates. The initial input state of the clones defines the asymmetry among all output clones. Although the generalized circuits do not perform universally, the averaged fidelities over a uniform distribution of all possible input cloning states saturate the optimal fidelity tradeoff relations of universal asymmetric cloning.