Optimal Universal N-M Cloning: Difference between revisions

This [[example protocol]] achieves the functionality of [[Quantum Cloning]]. Symmetric or Optimal Universal <math>N \rightarrow M</math> quantum cloning machine (QCM) transformation, acting on N original qubits, <math>(M - N)</math> blank qubits and an extra system which usually contains the states of the QCM itself, and produces M identical copies. Mathematically, this transformation is a [[Unitary transformation]] (It preserves the inner product). This machine is universal meaning it is not depending on the input states and works for all the possible inputs. Also, the machine is symmetric so all the output clones are the same and have the same [[fidelity]] with the original states. We investigate the optimal protocol which has the maximum possible average fidelity over all the states (produces best clones in average for all of the states).

==Assumptions==

* We assume that all of the original states are identical and also all of the output copies will be identical at the end of the protocol (In other words, the final output state belongs to the symmetric subspace of M qubits).