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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.
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 anillary 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.