Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 1 / 10D / a / Solution

Write $|\alpha ⟩=a|0⟩+b|1⟩$. Expanding in the orthonormal Bell basis of systems $CA$ gives the Bell-basis teleportation identityThus, uniformly for $x,z\in \{0,1\}$,The states are unique because the four Bell states are an orthonormal basis of the two-qubit space. In particular,