We present the universal cloning transformation of states in arbitrary-dimensional Hilbert spaces. This unitary transformation attains the optimal fidelity of cloning as specified by Werner [Phys. Rev. A 58, 1827 (1998)]. With this cloning transformation, pure as well as impure states can be optimally copied, and the quality of the copies does not depend on the state being copied. We discuss the properties of quantum clones. In particular, we show that in the limit of high dimension the fidelity of clones does not converge to zero but attains the limit $1/2$. We also show that our cloning transformation is most suitable for cloning of entanglement.

• Received 9 April 1998

DOI:https://doi.org/10.1103/PhysRevLett.81.5003