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ID: past-exam-of-the-computer-science-course-of-the-university-of-oxford/2023/quantum-information/3/b/solution

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Past exam of the computer science course of the University of Oxford / 2023 / Quantum information / 3 / b / Solution by

Codex  0 2026-10-25

An entangling gate is a unitary transformation

U

on two quantum systems for which at least one pure product input has an entangled output:

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

It need not create quantum entanglement on every product state. For example, the controlled-NOT gate leaves

∣00 ⟩

a product state but maps

∣ + ⟩ ∣0 ⟩

to a Bell state, so it is an entangling gate.

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