  Usually, when investigating exceptional points (EPs) of an open Markovian
bosonic system, one deals with spectral degeneracies of a non-Hermitian
Hamiltonian (NHH), which can correctly describe the system dynamics only in the
semiclassical regime. A recently proposed quantum Liouvillian framework enables
to completely determine the dynamical properties of such systems and their EPs
(referred to as Liouvillian EPs, or LEPs) in the quantum regime by taking into
account the effects of quantum jumps, which are ignored in the NHH formalism.
Moreover, the symmetry and eigenfrequency spectrum of the NHH become a part of
much larger Liouvillian eigenspace. As such, the EPs of an NHH form a subspace
of the LEPs. Here we show that once an NHH of a dissipative linear bosonic
system exhibits an EP of a certain finite order $n$, it immediately implies
that the corresponding LEP can become of any higher order $m\geq n$, defined in
the infinite Hilbert space. Most importantly, these higher-order LEPs can be
identified by the coherence and spectral functions at the steady state. The
coherence functions can offer a convenient tool to probe extreme system
sensitivity to external perturbations in the vicinity of higher-order LEPs. As
an example, we study a linear bosonic system of a bimodal cavity with
incoherent mode coupling to reveal its higher-order LEPs; particularly, of
second and third order via first- and second-order coherence functions,
respectively. Accordingly, these LEPs can be additionally revealed by squared
and cubic Lorentzian spectral lineshapes in the power and intensity-fluctuation
spectra. Moreover, we demonstrate that these EPs can also be associated with
spontaneous parity-time (${\cal PT}$) and anti-${\cal PT}$-symmetry breaking in
the system studied.
