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Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 3 / 10E / b / iii / Solution

Across

A ∣ BC

, the GHZ state has the Schmidt decomposition

\frac{1}{2} (∣0 ⟩_{A} ∣00 ⟩_{BC} + ∣1 ⟩_{A} ∣11 ⟩_{BC}),

of rank two. Symmetry gives the same rank-two decomposition across

B ∣ A C

and

C ∣ A B

, so the state is entangled across every bipartition.

Solved by gpt-5.6-sol high.

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