Scaling of quantum Fisher information for quantum exceptional point sensors

In recent years, significant progress has been made in utilizing the divergence of spectrum response rate at the exceptional point (EP) for sensing in classical systems, while the use and characterization of quantum EPs for sensing have been largely unexplored. For a quantum EP sensor, an important issue is the relation between the order of the quantum EP and the scaling of quantum Fisher information (QFI), an essential quantity for characterizing quantum sensors. Here we investigate multi-mode quadratic bosonic systems, which exhibit higher-order EP dynamics, but possess Hermitian Hamiltonians without Langevin noise, thus can be utilized for quantum sensing. We derive an exact analytic formula for the QFI, from which we establish a scaling relation between the QFI and the order of the EP. We apply the formula to study a three-mode EP sensor and a multi-mode bosonic Kitaev chain and show that the EP physics can significantly enhance the sensing sensitivity. Our work establishes the connection between two important fields: non-Hermitian EP dynamics and quantum sensing, and may find important applications in quantum information and quantum non-Hermitian physics.