 Solution

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

A bipartite pure state is entangled exactly when it is not a product state: there are no normalized quantum states

∣ u ⟩_{A}, ∣ v ⟩_{B}

such that

∣ ψ ⟩_{A B} = ∣ u ⟩_{A} \otimes ∣ v ⟩_{B} .

Equivalently, its Schmidt rank exceeds one, or either reduced density matrix is a mixed state. This definition concerns quantum entanglement across the specified division into systems

A

and

B

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