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We investigate the parameter estimation problems of two-atom system driven by the phase noise lasers (PNLs) environment. And we give a general method of numeric solution to handle the problems of atom system under the PNLs environment. The calculation results of this method on Quantum Fisher Information (QFI) are consistent with our former results. Moreover, we consider the dipole–dipole ( d – d ) interaction between the atoms under PNLs environment with the collective decay, and the results show that larger  d – d  interaction and smaller collective decay rate lead to larger QFI of the two-atom system. So the collective decay will destroy the QFI while the  d – d  interaction will preserve the QFI, these results can be used to protect the QFI of two-atom system driven by the PNLs environment.

Quantum Fisher information of two atoms with dipole–dipole interaction under the environment of phase noise lasers