Fisher information and spin squeezing in the Lipkin-Meshkov-Glick model

Jian Ma and Xiaoguang Wang

Phys. Rev. A 80, 012318 – Published 17 July 2009

Abstract

Fisher information, which lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement [L. Pezzé and A. Smerzi, Phys. Rev. Lett. 102, 100401 (2009)]. We use Fisher information to distinguish and characterize behaviors of ground state of the Lipkin-Meskhov-Glick model, which displays a second-order quantum phase transition between the broken and symmetric phases. We find that the parameter sensitivity of the system attains the Heisenberg limit in the broken phase, while it is just around the shot-noise limit in the symmetric phase. Based on parameter estimation, Fisher information provides us a useful approach to the quantum phase transition.