OPTIMAL UNIVERSAL QUANTUM CLONING AND STATE ESTIMATION

We derive a tight upper bound for the fidelity of a universal N --> M qubit cloner, valid for any M greater than or equal to N, where the ou tput of the cloner is required to be supported on the symmetric subspa ce. Our proof is based on the concatenation of two cloners and the con nection between quantum cloning and quantum state estimation. We gener alize the operation of a quantum cloner to mixed and/or entangled inpu t qubits described by a density matrix supported on the symmetric subs pace of the constituent qubits. We also extend the validity of optimal state estimation methods to inputs of this kind. [S0031-9007(98)07141 -5].