  Quantum Fisher information characterizes the phase sensitivity of qubits in
the spin-boson model with a finite bandwidth spectrum. In contrast with
Markovian reservoirs, the quantum Fisher information will flow from the
environments to qubits after some times if the bath parameter $s$ is larger
than a critical value which is related to temperatures. The sudden change
behavior will happen during the evolution of the quantum Fisher information of
the maximal entanglement state in the non-Markovian environments. The sudden
change times can be varied with the change of the bath parameter $s$. For a
very large number of entangled qubits, the sudden change behavior of the
maximal quantum Fisher information can be used to characterize the existence of
the entanglement. The metrology strategy based on the quantum correlated state
leads to a lower phase uncertainty when compared to the uncorrelated product
state.
