Abstract
Quantum metrology and quantum sensing aim to use quantum properties to enhance measurement precision beyond what could be classically achieved. Here, we demonstrate how the analysis of the phase space structure of the classical limit of Kerr parametric oscillators can be used for determining control parameters values that lead to the squeezing of the uncertainty in position and the amplification of the quantum Fisher information. We also explore how quantum sensing can benefit from excited-state quantum phase transitions, even in the absence of a conventional quantum phase transition. The system that we consider models exciton-polariton condensates and superconducting circuits, making our study relevant for potential experimental applications.