Optimal Universal N-M Cloning: Difference between revisions

'''Tags:'''Building blocks, [[Quantum Cloning]], Universal Cloning, optimal cloning, N to M cloning, symmetric cloning, copying quantum states, quantum functionality, [[Asymmetric Universal 1-2 Cloning|Asymmetric Cloning]], [[Probabilistic Cloning|Probabilistic Cloning]]

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.

**<math>|\psi\rangle^{\otimes N}:</math> N initial states

**<math>|\psi^{\perp}\rangle:</math> The state orthogonal to <math>|\psi\rangle</math>

**<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

*'''The protocol-'''

**assumes 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).

*'''Special case of 1 qubit to 2 qubits:''' <math>F_{1 \rightarrow 2} = \frac{5}{6}</math>

'''Input:''' j qubits where <math>R_{j}</math> are ancillary and internal states of the QCM.