  A pair of coupled quantum harmonic oscillators, one subject to a gain one to
a loss, is a paradigmatic setup to implement PT-symmetric, non-Hermitian
Hamiltonians in that one such Hamiltonian governs the mean-field dynamics for
equal gain and loss strengths. Through a full quantum description (so as to
account for quantum noise) here is shown that when the system starts in any
two-mode coherent state, including vacuum, there appear quantum correlations
(QCs) without entanglement, as measured by the Gaussian discord. When the loss
rate is above a threshold, once generated QCs no more decay. This occurs in a
wide region of parameters, significantly larger than that where the full
quantum dynamics is stable. For equal gain and loss rates, in particular, QCs
decay in the exact phase (including the exceptional point) and are stable in
the broken phase.
