We analyze the quantum Fisher information (QFI) and entanglement of the ground state for the XY model. The QFI determines the precision in parameter estimations, moreover, it is a criterion of entanglement. The scaling behaviors of the QFI are studied both at the critical point and in different phases. In the symmetry-broken phase, the QFI scales proportional to the square of the system size, while in the symmetric phase, it is nearly independent of the system size. The study of QFI not only reveals the distinct entanglement properties of the XY model in different phases, but also shows that the ground state of the XY model can be used to perform Heisenberg-limit parameter estimation.
We investigate the quantum Fisher information (QFI) of symmetric states for spin-s particles. We derive the maximal QFI, and find that quantum spin correlations are essential ingredients of the maximal QFI. We make applications to the generalized one-axis twisting model. The results show that the redistributions of uncertainties on the basis of the quantum correlations in the multiqubit system are useful for sub-shot-noise phase sensitivity. Furthermore, for high-spin (s > 1/2) composite systems, we find a sufficient criterion for entanglement.
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