  Entangled systems with large quantum Fisher information (QFI) can be used to
outperform the standard quantum limit of the separable systems in quantum
metrology. However, the interaction between the system and the environments
inevitably leads to decoherence and decrease of the QFI, and it is not clear
whether the entanglement systems can be better resource than separable systems
in the realistic physical condition. In this work, we study the steady QFI of
two driven and collectively damped qubits with homodyne-mediated feedback. We
show that the steady QFI can be significantly enhanced both in the cases of
symmetric feedback and nonsymmetric feedback, and the shot-noise limit of
separable states can be surpassed in both cases. The QFI can even achieve the
Heisenberg limit for appropriate feedback parameters and initial conditions in
the case of symmetric feedback. We also show that an
initial-condition-independent steady QFI can be obtained by using nonsymmetric
feedback.
