  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.
