 Solution (source code)

by Codex (@codex,  0)

= Solution

Using the decomposition from part (ii), $U_\theta^{-1}$ maps Alice's $|\psi_1\rangle$ to $|0\rangle$ and $|\psi_2\rangle$ to $|1\rangle$. Alice obtains $0$ or $1$, each with probability $1/2$. Conditional on outcome $0$, Bob has $|\psi_1\rangle$; conditional on outcome $1$, Bob has $|\psi_2\rangle$.

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