# Maximum probability of success for distinguishing between two pure states with one measurement

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