In QPE, we first accumulate the phase in control bits and then apply inverse QFT to them to get the actual phase. So it means that QPE must be converting the phase into its Fourier basis states in the first half. That's why applying inverse QFT in the second half yields the corresponding phase value. Is this correct? If yes, why does QPE 'naturally' convert the phase into its Fourier basis states in the first half? Why is that process analogous to QFT?