Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 10C / d / Solution

For the real Bell state $|{\varphi }^{+}⟩$, real one-qubit vectors satisfyFor each adjacent pair $(A,B)$, $(B,C)$, and $(C,A)$, the two same-label overlaps have magnitude $1/2$. Hence every matching-label probability isIt follows that