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

Relative Phase Distribution and the Precision of Optical Phase Sensing in Quantum Metrology