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Suppose you have the states such that $\langle \phi | \theta \rangle = cos(x)$ and you have one measurement to distinguish between the two. It is claimed that the probability of success at guessing correctly is $P = \frac{1+sin(x)}{2}$. How do you arrive at this probability?

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I think this is a really simple problem. I have a feeling I have seen this proof before, but I don't remember where. :p –  Catherine Holloway Apr 15 '12 at 14:32

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up vote 3 down vote accepted

There are nice explanations in Terry Rudolph's quantum information lecture notes, which should be publicly available here and here (the relevant ones), but tell me if they're not.

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Awesome! thanks! That is exactly what I was looking for. –  Catherine Holloway Apr 15 '12 at 16:09

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