Protection of quantum Fisher information in entangled states via classical driving

Quantum entanglement can offer a quadratic enhancement in the precision of parameter estimation. We here study the protection of quantum Fisher information (QFI) of the phase parameter in entangled-atom states within the framework of independently dissipative environments and driven individually by classical fields. It is shown that the QFI of the phase parameter can be protected effectively only when the classical fields that drive all atoms are suitably strong, and if one of them vanishes or is very weak, then the ability of protection loses, no matter how strong the other driving fields are. We also study the evolution of fidelity of the entangled state itself and find that though the protections of QFI and quantum states are two different notions, the method can also be used to protect quantum states effectively when the driving fields are suitably strong.