Quantum Fisher Information for su (2) Atomic Coherent States and su (1,1) Coherent States

We investigate quantum Fisher information (QFI) for su (2) atomic coherent states and su(1, 1) coherent states. In this work, we find that for su(2) atomic coherent states, the QFI with respect to 79 (F-upsilon) is independent of phi, the QFI with respect to phi (F phi) is governed by 79. Analogously, for su(1, 1) coherent states, TF is independent of co, and F-phi, is determined by r. Particularly, our results show that Tv, is symmetric with respect to upsilon = pi/2 for su(2) atomic coherent states. And for su(1, 1) coherent states, Tv, also possesses symmetry with respect to r = 0.