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We derive upper bounds on the quantum Fisher information in interferometrywith $N$ subsystems, e.g. two-level atoms or Gaussian modes, in the presence ofarbitrarily correlated Gaussian dephasing including independent and collectivedephasing. The derived upper bound enables us to analyse the Fisher informationasymptotic behaviour when $N\rightarrow\infty$. Dephasing introduces randomphases to subsystems dynamics, which lowers the precision of estimating thephase difference $\phi$ in an interferometer. The method presented usesBayesian estimation of the random phases and eliminates dephasing noise bycalculating their weighted arithmetic mean, which correponds to the phase$\phi$ estimated in interferometry.

Upper bounds on the quantum Fisher Information in the presence of general dephasing