Quantum Computation: extracting information from entangled state

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Hello,

I have a state of two registers (A and B) which is in the following form respect to the computational basis:

[tex]|v> = \frac{1}{N}\sum_{k=0}^{N-1} |k>_A |f(k)>_B[/tex]

I don't know how to prepare this state, it is externally given. I would like to extract the value of [tex]f(\hat{x})[/tex] for some known [tex]\hat{x}[/tex] .

An obvious solution is to measure both registers respect the computational basis and check whether result obtained from A is [tex]\hat{x}[/tex] . This would succed with probability 1/N .

I thought of using some form of Grover-like amplitude amplification to increase the success probability, but since I don't have access to an operator which produces |v> , I can't costruct the appropriate reflection operators.

Any thoughts?
 

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