  We show that the loss of nonclassicality (including quantum entanglement)
cannot be compensated by the (incoherent) amplification of PT-symmetric
systems. We address this problem by manipulating the quantum fluctuating forces
in the Heisenberg-Langevin approach. Specifically, we analyze the dynamics of
two nonlinearly coupled oscillator modes in a PT-symmetric system. An
analytical solution allows us to separate the contribution of reservoir
fluctuations from the evolution of quantum statistical properties of the modes.
In general, as reservoir fluctuations act constantly, the complete loss of
nonclassicality and entanglement is observed for long times. To elucidate the
role of reservoir fluctuations in a long-time evolution of nonclassicality and
entanglement, we consider and compare the predictions from two alternative
models in which no fatal long-time detrimental effects on the nonclassicality
and entanglement are observed. This is so as, in the first semiclassical model,
no reservoir fluctuations are considered at all. This, however, violates the
fluctuation-dissipation theorem. The second, more elaborated, model obeys the
fluctuation-dissipation relations as it partly involves reservoir fluctuations.
However, to prevent from the above long-time detrimental effects, the reservoir
fluctuations have to be endowed with the nonphysical properties of a sink
model. In both models, additional incorporation of the omitted reservoir
fluctuations results in their physically consistent behavior. This behavior,
however, predicts the gradual loss of the nonclassicality and entanglement.
Thus the effects of reservoir fluctuations related to damping cannot be
compensated by those related to amplification.
