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.
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