  We present a rigorous and quantum-consistent description of dispersive
non-Hermitian optical bilayers in the framework of the canonical quantization
scheme. Then we investigate the propagation of a normally incident squeezed
coherent state of light through such media, particularly at a frequency for
which the bilayers become parity-time (PT) symmetric. Furthermore, to check the
realization of PT-symmetry in quantum optics, we reveal how dispersion and
loss/gain-induced noises and thermal effects in such bilayers can affect
quantum features of the incident light, such as squeezing and sub-Poissonian
statistics. The numerical results show thermally-induced noise at room
temperature has an insignificant effect on the propagation properties in these
non-Hermitian bilayers. Moreover, tuning the bilayers loss/gain strength, we
show that the transmitted squeezed coherent states through the structure can
retain to some extent their nonclassical characteristics, specifically for the
frequencies far from the emission frequency of the gain layer. Furthermore, we
demonstrate, only below a critical value of gain, quantum optical effective
medium theory can correctly predict the propagation of quantized waves in
non-Hermitian and PT-symmetric bilayers.
