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.
Demonstration of deterministic and high fidelity squeezing of quantum information.Physical Review A—Atomic, Molecular, and Optical Physics, 76(6):060301, 2007
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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.