Optimal Universal Quantum Cloning and State Estimation

@article{Bru1998OptimalUQ,
  title={Optimal Universal Quantum Cloning and State Estimation},
  author={Dagmar Bru{\ss} and Artur K. Ekert and Chiara Macchiavello},
  journal={Physical Review Letters},
  year={1998},
  volume={81},
  pages={2598-2601}
}
We derive a tight upper bound for the fidelity of a universal N ! M qubit cloner, valid for any M $ N, where the output of the cloner is required to be supported on the symmetric subspace. Our proof is based on the concatenation of two cloners and the connection between quantum cloning and quantum state estimation. We generalize the operation of a quantum cloner to mixed and /or entangled input qubits described by a density matrix supported on the symmetric subspace of the constituent qubits… 
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