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The chain of reasoning runs something like this: Assume that the distributions $\mu_0(\lambda)$ and $\mu_+(\lambda)$ overlap in $\Delta\subset\Lambda$, so with probability $q$ preparing $|0⟩$ will produce a state $\lambda$ consistent with $|+⟩$ and vice versa. Assume that the two systems can be prepared independently. Therefore, with probability $q$ the ...

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