  We analyse two quantum systems with hidden parity-time (PT) symmetry: one is
an optical device, whereas another is a superconducting microwave-frequency
device. To investigate their symmetry, we introduce an equilibrium frame, in
which loss and gain terms for a given Hamiltonian are balanced. We show that
the non-Hermitian Hamiltonians of both systems can be tuned to reach an
exceptional point (EP), i.e., the point in parameter space at which a
transition from broken to unbroken hidden PT symmetry takes place. We calculate
a degeneracy of a Liouvillian superoperator, which is called the Liouvillian
exceptional point (LEP), and show that, in the optical domain, LEP is
equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also
report breaking the equivalence between LEP and HEP by a non-zero number of
thermal photons for the microwave-frequency system.
