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I'm not sure that I agree with what is presented as the solution (although the final answer seems OK). Let me explain what I would do. That task gives you 3 states $|A\rangle$, $|B\rangle$ and $|C\rangle$. You want a POVM that, for example, cannot give the answer "0" is the state was in $|A\rangle$, cannot give the answer "1" if the state ...


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