Quantum Fisher Information Gap for Systems with Nonlinear Hamiltonians**Supported by the National Key Research and Development Program of China under Grant Nos. 2017YFA0304202 and 2017YFA0205700, the National Natural Science Foundation of China under Grant No. 11875231, and the Fundamental Research Funds for the Central Universities under Grant No. 2018FZA3005. B.L. acknowledges support by the Thirteenth Five-year Planning Project of Jilin

Abstract

Quantum Fisher information (QFI) gap characterizes the stability of QFI to space directions. We study the QFI distributions and QFI gap for quantum states generated from nonlinear Hamiltonians for both spin and bosonic systems. We find that the same spin-squeezing parameter (or principle squeezing parameter) corresponds to two different values QFI gap, and the locations of all extreme points of the QFI are explicitly given.