Relative phase distribution and the precision of optical phase sensing in quantum metrology

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