Abstract

The explicit transformations of the 1 → 3 optimal universal quantum cloning and the optimal phase-covariant quantum cloning in d-dimensions are presented, and the dimensionalities of their ancillary systems are both d-dimensions. As d→∞, their clone fidelities move toward 1/3, showing a classical limit for the fidelity of quantum cloning. Based on the reduction of the unitary transformation of quantum cloning, the transformation of the 1→M=d+1 optimal economical phase-covariant quantum cloning in d-dimensions is derived, and the clone fidelity is covered by the theoretical value.

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