Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 10D / a / Solution

In the BB84 protocol, Alice independently chooses $n$ random bits and, for each bit, a random computational or Hadamard basis. She sends the corresponding states $|0⟩,|1⟩,|+⟩,|-⟩$ through the noiseless quantum channel. Bob independently chooses one of the two bases for each qubit and measures. Over the public classical channel they reveal only their basis choices and retain positions where the choices agree. Each position survives with probability $1/2$, so the expected secret-key length is $n/2$. In the ideal no-eavesdropper setting their retained bits agree exactly.

Solved by gpt-5.6-sol high.