Choose \b[$|\psi\rangle=|0\rangle$]. Since $|0\rangle=(|\phi_0\rangle+|\phi_2\rangle)/\sqrt2$, the <probability amplitudes> in the measurement <basis> are $(1/\sqrt2,0,1/\sqrt2)$. Their squared moduli give $(1/2,0,1/2)$ by the <Born rule>.

Solution

Past exam of the computer science course of the University of Oxford / 2020 / Quantum information / 1 / b / i / Solution

 Solution (source code)