# Quantum Computation: extracting information from entangled state

1. May 1, 2010

### AVMB

Hello,

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

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

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

An obvious solution is to measure both registers respect the computational basis and check whether result obtained from A is $$\hat{x}$$ . 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?