Past exam of the computer science course of the University of Oxford / 2022 / Quantum information / 3 / d / i / Solution

For input $|0{⟩}_S$, the controlled-NOT gate fixes $|00{⟩}_{SC}$, which is the ideal two-copy pure state. Thus its global cloning fidelity is $F_0=1$. For input $|+{⟩}_S$, the actual output is the Bell state $|{\varphi }_{+}⟩$, whereas the desired output is $|++⟩$. Their overlap isWith the given equal input probabilities,These values use the specified squared quantum fidelity for the full output, rather than a one-copy marginal fidelity.