 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2022/quantum-information/3/d/i/solution

For input

∣0 ⟩_{S}

∣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

∣ ϕ_{+} ⟩

, whereas the desired output is

∣ + + ⟩

. Their overlap is

⟨ + + ∣ ϕ_{+} ⟩ = \frac{1}{2}, F_{+} = \frac{1}{2} .

With the given equal input probabilities,

F_{0} = 1, F_{+} = \frac{1}{2}, \overline{F} = \frac{1}{2} (1 + \frac{1}{2}) = \frac{3}{4} .

These values use the specified squared quantum fidelity for the full output, rather than a one-copy marginal fidelity.

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