Dynamical quantum Fisher information in the Ising model

In terms of quantum Fisher information, we discuss the dynamics of quantity χ 2 of the Ising model. The inequality χ 2 < 1 detects the class of entangled states which are useful for sub-shot-noise sensitivity. All the exact dynamics of the expectations of collective spin operators are derived. The minimum χ 2 in the plane perpendicular to the mean spin direction is analytically given. We find that χ 2 does not depend on the system size N when N ≥ 4 . Except for the periodic points, the evolution states are always entangled and useful for the sub-shot-noise phase estimation.