Past exam of the computer science course of the University of Oxford / 2020 / Quantum information / 3 / c / Solution

The phase oracle multiplies an unmarked basis vector by $+1$ and a marked one by $-1$. Thus the state after the oracle isIts squared norm is $(S_0+S_1)/N=1$. All computational outcomes would still have probability $1/N$ if measured at this point: the oracle has changed the relative phase, not the magnitudes of the amplitudes. The following reflection converts that phase information into a changed probability distribution through quantum interference.