  One of the quantum metrology goals is to improve the precision in the
measurement of a small optical phase introduced in one optical mode in an
interferometer, i.e., phase sensing. In this paper, we obtain the relative
phase distribution introduced by Luis and S\'anchez-Soto (LSS) [Phys. Rev. A
$\mathbf{53}$, 495 (1996)] for several two-mode pure quantum light states
useful in quantum metrology. We show that, within the numerical precision of
our calculations, the Fisher information obtained from the LSS relative phase
distribution is equal to the quantum Fisher information for the considered
states (the average difference for the tested states is smaller than 0.1%). Our
results indicate that the LSS relative phase distribution can be used to
predict the minimum uncertainty possible in the process of phase sensing in
quantum metrology, since this uncertainty depends on the quantum Fisher
information, at least for pure states.
