A pr 2 00 1 Singlet states and the estimation of eigenstates and eigenvalues of an unknown Controlled-U gate

We consider several problems that involve finding the eigenvalues and generating the eigenstates of unknown unitary gates. We first examine Controlled-U gates that act on qubits and assume that we know the eigenvalues. It is then shown how to use singlet states to produce qubits in the eigenstates of the gate. We then remove the assumption that we know the… (More)