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

By Jian Ma, Xiaoguang Wang. 2009

155 citations recorded by the source corpus.

Fisher information, which lies at the heart of parameter estimation theory, was recently found to have a close relation with multipartite entanglement [L. Pezze 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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/19bba3d6f09645a7b7992beaacbb17904406996b

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum metrology with nonclassical states of atomic ensembles (2016, background): “Entanglement (Buonsante et al., 2012; Ma and Wang, 2009; Mazzarella et al., 2011; Orús et al., 2008; Vidal et al., 2004) and fluctuations of the order parameter (Ziń et al., 2008) approaching the transition point have been extensively studied.”
Measuring multipartite entanglement through dynamic susceptibilities (2015, methodology): “A simple example to demonstrate the insensitivity towards thermal phase transitions is provided by the fully-connected transversefield Ising model, Jlj = 1/N , ∀ l, j [17, 37], similar to the model describing the experiments of Ref.”
Quantum spin squeezing (2010, methodology): “uantum metrology. In this section, we rst introduce the QFI [236,172,237,238], which determines the precision of the parameter estimation. Then, we discuss the relation between QFI and spin squeezing [239,240,241,242]. Finally, we discuss the applications of spin squeezing and QFI in entanglement en”