Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 15E / b / Solution

Conditional on Alice and Bob using the same basis, Eve chooses the wrong basis with probability $2/3$, then Bob disagrees with probability $1/2$, so the conditional error is $1/3$. Alice and Bob match with probability $1/3$, hence the per-transmission detection probability is $1/9$.

Solved by gpt-5.6-sol high.