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Optimal Universal N-M Cloning
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==Notation== **<math>|\psi\rangle^{\otimes N}:</math> N initial states **<math>|\psi^{\perp}\rangle:</math> The state orthogonal to <math>|\psi\rangle</math> **<math>R_{j}:</math> ancillary and internal states of the QCM **<math>U_{N,M}:</math> Unitary operation describing the QCM **<math>F_{N \rightarrow M}:</math> Fidelity of the USQCM showing how close the M output copies are to the N original states
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