Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 3 / 15E / a / Solution

Across the cut $A|BC$, the two conditional $BC$ vectors $\alpha |00⟩$ and $\gamma |00⟩+\beta |11⟩$ are linearly independent when $\alpha \beta \ne 0$, so the Schmidt rank exceeds one. Hence the state cannot be a three-qubit product for any $\gamma$.