  A two-mode optical parity-time (PT) symmetric system, with gain and damping,
described by a quantum quadratic Hamiltonian with additional small Kerr-like
nonlinear terms, is analyzed from the point of view of nonclassical-light
generation. Two kinds of stationary states with different types of
(in)stability are revealed. Properties of one of these are related to the
presence of semiclassical exceptional points, i.e., exotic degeneracies of the
non-Hermitian Hamiltonian describing the studied system without quantum jumps.
The evolution of the logarithmic negativity, principal squeezing variances, and
sub-shot-noise photon-number correlations, considered as entanglement and
non-classicality quantifiers, is analyzed in the approximation of
linear-operator corrections to the classical solution. Suitable conditions for
nonclassical-light generation are identified in the oscillatory regime,
especially at and around exceptional points that considerably enhance the
nonlinear interaction and, thus, the non-classicality of the generated light.
The role of quantum fluctuations, inevitably accompanying attenuation and
amplification in the evolution of quantum states, is elucidated. The evolution
of the system is analyzed for different initial conditions.
