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

After transmission Alice and Bob announce bases, retain matching-basis bits, reveal a random sample, and abort if its error rate is too large; privacy amplification and error correction produce the key. A Breidbart intercept-resend causes error $1/4$ conditional on matching Alice and Bob bases. Since matching occurs with probability $1/2$, one transmitted qubit detects Eve with probability $1/8$.

Solved by gpt-5.6-sol high.