For single-parameter phase estimation, the success-probability-weighted quantum Fisher information of any non-Gaussian state heralded from Gaussian resources through passive linear optics is no larger than the quantum Fisher information of the original Gaussian input.
Few-cycle vacuum squeezing in nanophoton- ics.Science, 377(6612):1333–1337, 2022
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Fundamental limits of parameter estimation with heralded optical non-Gaussian states generated from Gaussian resources
For single-parameter phase estimation, the success-probability-weighted quantum Fisher information of any non-Gaussian state heralded from Gaussian resources through passive linear optics is no larger than the quantum Fisher information of the original Gaussian input.