Past exam of the laser science and quantum information processing course of the University of Oxford / 2019 / 4 / b / ii

Bob must discard both results. An unread X measurement gives ${\rho }_X=p_{+}|+⟩⟨+|+p_{-}|-⟩⟨-|$. Each of these two X eigenstates gives Z outcomes with probabilities $1/2,1/2$. The final unread Z measurement therefore givesEquivalently, in the Bloch-vector description the first measurement retains only the X component, and the second retains only the Z component, leaving none. The final state is independent of the original $\alpha ,\beta$.