  We utilize quantum Fisher information to investigate the damping parameter
precision of a dissipative qubit. PT symmetric non-Hermitian Hamiltonian is
used to enhance the parameter precision in two models: one is direct PT
symmetric quantum feedback; the other is that the damping rate is encoded into
a effective PT symmetric non-Hermitian Hamiltonian conditioned on the absence
of decay events. We find that compared with the case without feedback and with
Hermitian quantum feedback, direct PT symmetric non-Hermitan quantum feedback
can obtain better precision of damping rate. And in the second model the result
shows that the uncertainty of damping rate can be close to 0 at the exceptional
point. We also obtain that non-maximal multiparticle entanglement can improve
the precision to reach Heisenberg limit.
