 Solution

ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2022/quantum-information/2/a/iii/solution

An entangling gate is a unitary operator on two quantum systems for which some pure product input is mapped to an entangled state:

\exists ∣ u ⟩_{A}, ∣ v ⟩_{B} : U (∣ u ⟩_{A} \otimes ∣ v ⟩_{B}) is entangled .

It need not create quantum entanglement from every product state. For example, a controlled-NOT gate entangles

∣ + ⟩ ∣0 ⟩

∣00 ⟩

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