I have the next promise problem in quantum cryptography:

We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $

  where Yes instances are those for which: $$ |<\phi_1,\phi_2>| \leq \alpha$$

and No instances are those for which: $$|<\phi_1,\phi_2>|\geq \beta$$

I need to devise a quantum circuit that accepts Yes instances with probability at least $p$, and No instances with at most probability $q$ for some $q<p$.

Do you have some reference for this promise problem?

Thanks in advance.

Consider this problem in quantum cryptography:

We have two pure states $\phi_1,\phi_2$ as input and constants $0 \leq \alpha <\beta \leq 1 $, where "Yes instances" are those for which $$\left|\left<\phi_1,\phi_2\right>\right| \leq \alpha$$ and "No instances" are those for which $$\left|\left<\phi_1,\phi_2\right>\right|\geq \beta$$

I need to devise a quantum circuit that accepts "Yes instances" with probability at least $p$, and "No instances" with at most probability $q$ for some $q<p$.

How can I do this? Is there a reference in which this problem is solved?

Thanks in advance.