Optimal Cloning of Pure States, Judging Single Clones

Abstract

We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state σinto M>N systems of the same kind, in an approximation of the M-fold tensor product of the state σ. In a previous paper it was shown that this problem has a unique optimal solution, when the quality of the output is judged by arbitrary measurements, involving also the correlations between the clones. We show in this paper, that if the quality judgement is based solely on measurements of single output clones, there is again a unique optimal cloning device, which coincides with the one found previously.

16 Pages, REVTeX

References in corpus (9)

• Optimal Quantum Cloning Machines
• Quantum telecloning and multiparticle entanglement
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Quantum cloning and the capacity of the Pauli channel
• Quantum cloning without signaling
• Quantum copying: Fundamental inequalities
• Optimal Copying of One Quantum Bit
• No-cloning of Orthogonal States in Composite Systems

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