Consider we have a single copy of a state,
\begin{equation} |\psi\rangle = b |0\rangle_{anc} \otimes |B\rangle_{tar} + g |1\rangle_{anc} \otimes |G\rangle_{tar} \end{equation} where the amplitudes $b,g$ are unknown. By measuring the ancilla system if we observe a bit flip then we obtain the desired good state $|G\rangle$ in the target system. Is it possible to apply the amplitude amplification algorithm on $|\psi\rangle$ to boost the probability of measuring $|1\rangle$ in the ancilla system?
