  Understanding the interplay between quantum coherence and non-Hermitian
features would enable the devising of quantum technologies based on dissipative
systems. In turn, quantum coherence can be characterized in terms of the
language of multiple quantum coherences (MQCs) originally developed in
solid-state nuclear magnetic resonance (NMR), nowadays applied to the detection
of quantum chaos, and to the study of criticality in many-body quantum systems.
Here we show the usefulness of MQCs for probing equilibrium phase transitions
in non-Hermitian systems. To do so, we investigate the connection of quantum
coherences and critical points for several paradigmatic non-Hermitian
Hamiltonians. For a non-Hermitian two-level system, MQCs witness the
parity-symmetry breaking phase transition from the unbroken to the broken
phase. Furthermore, for the non-Hermitian transverse field Ising model, MQCs
capture the Yang-Lee phase transition in which the ground state energy acquires
a nonzero imaginary component. For the disordered Hatano-Nelson (HN) model with
periodic boundary conditions, MQCs testify the emergence of mobility edges in
the spectrum of this model. In addition, MQCs signal the topological phase
transition exhibited by the complex energy spectra of the disorder-free HN
model. Finally, we comment on experimentally probing phase transitions in NMR
systems realizing non-Hermitian Hamiltonians. Our results have applications to
non-Hermitian quantum sensing, quantum thermodynamics, and in the study of the
non-Hermitian skin effect.
