Global cloning fidelity (source code)

= Global cloning fidelity
{title2=$F_{\mathrm{global}}(\phi)=|\langle\phi|^{\otimes2}U|\phi,0\rangle|^2$}

For a <quantum cloning> device with <pure state> output $U|\phi,0\rangle$, the global cloning fidelity is its <squared quantum fidelity> with the desired joint two-copy <pure state>. It is the <probability> that a joint projector test for two ideal copies accepts the actual output. It differs from a one-clone marginal fidelity: correlations between the output <qubits> affect the joint overlap. For a <controlled-NOT gate> with input $|+\rangle|0\rangle$, the output is a <Bell state> and its global cloning fidelity with $|++\rangle$ is $1/2$; for input $|0\rangle|0\rangle$ it is one.