Past exam of the short options paper of the physics Prelims of the University of Oxford / 2022 / S03 / 2 / d / Solution

Send a beam through a vertical Stern-Gerlach spin measurement apparatus, spatially resolve its two spin components, and block the negative-$z$ beam. The transmitted particles are prepared in $\boxed{|\uparrow ⟩}$. For an initially unpolarized beam, half the intensity survives ideally. This is conditional quantum state preparation by a projective measurement and filtering.