Ok! My question boils down to the comprehension of the quantum phase estimation algorithm. Is the following assertion correct?
In the quantum phase estimation:
1. If the input state is an eigenvector of the considered unitary, then we have the the phase corresponding to its eigenvalue (up to a given probability).
2. If the input state is not an eigenvector, then it is a "superposition" (linear combination) of the eigenvectors of the considered unitary. Then the output is a superposition of the corresponding eigenvalues.