\b[A secure key can be produced, at one ideal secret bit per copy.] The shared <Bell state> is pure, so the preceding factorization shows that Eve's purifying system is independent of it. Measuring both qubits in the <computational basis> gives matching outcomes $00$ or $11$, each with <probability> $1/2$. Neither party announces these key outcomes. Eve's state is the same for both possibilities, so each copy supplies a shared uniform private bit.

Solution

Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 53 / 4 / A / 1 / Solution

 Solution (source code)