Enhancing precision of damping rate by PT symmetric Hamiltonian

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.