Scaling of quantum Fisher information for quantum exceptional point sensors

In recent years, significant progress has been made in utilizing the spectrum divergence at the exceptional point for sensing in classical systems. However, the use and characterization of quantum exceptional points for sensing have been largely unexplored. This raises the question of the relationship between the order of the quantum exceptional point and the scaling of quantum Fisher information, an essential quantity for characterizing quantum sensor. Here we investigate multi-mode quartic Bosonic systems, which exhibit higher-order exceptional point dynamics, but possess Hermitian Hamiltonians without Langevin noise. We derive an exact analytic formula for the quantum Fisher information, from which we establish a scaling relation between the quantum Fisher information and the order of the exceptional point. Our work builds the connection among three important fields: non-Hermitian exceptional point dynamics, quantum sensing, and entangled squeezed states, and may find important applications in quantum sensing and quantum non-Hermitian physics.