Past exam of the computer science course of the University of Oxford / 2023 / Quantum information / 3 / a

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- Solution 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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