A Remark on the Optimal Cloning of An N-Level Quantum System

Abstract

We study quantum cloning machines (QCM) that act on an unknown N-level quantum state and make M copies. We give a formula for the maximum of the fidelity of cloning and exhibit the unitary transformations that realize this optimal fidelity. We also extend the results to treat the case of M copies from $N^{\prime }$ ($M>N^{\prime }$) identical N-level quantum systems.

8 pages, Latex

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