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Optimal Universal N-M Cloning
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==Outline== The steps of the protocol will be as follow: * Prepare your N original states and <math>(M - N)</math> blank states. This machine acts on these states and also on internal states of the QCM. * Perform the operation of the QCM which is a transformation taking these states to M identical states as close as possible to the original states. This unitary operation can be implemented by quantum gates (or other equivalent quantum computing models) *Discard the extra machine states that have been used in the previous step. Mathematically this means that you should <math>trace out</math> the states of the machine. The final output states will be the M approximately similar copies.
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