Choose \b[$|\psi\rangle=|\phi_2\rangle$]. Its <inner products> with the three measurement <vectors> are $(0,0,1)$, so the <Born rule> gives certainty for the outcome labelled 2 and zero <probability> for the other two outcomes. This uses the measurement <basis>, rather than assuming that its label 2 means the initial state must be the computational <vector> $|2\rangle$.

Solution

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

 Solution (source code)