  Attenuation and amplification are the most common processes for optical
communications. Amplification can be used to compensate the attenuation of the
complex amplitude of an optical field, but is unable to recover the coherence
lost, provided that the attenuation channel and the amplification channel are
independent. In this work, we show that the quantum coherence of an optical
filed can be regained if the attenuation channel and the amplification channel
share correlated noise. We propose an all-optical correlated noisy channel
relying on four-wave mixing process and demonstrate its capability of
recovering quantum coherence within continuous-variable systems. We
quantitatively investigate the coherence recovery phenomena for coherent states
and two-mode squeezed states. Moreover, we analyze the effect of other photon
losses that are independent with the recovery channel on the performance of
recovering coherence. Different from correlated noisy channels previously
proposed based on electro-optic conversions, the correlated noisy channel in
our protocol is all-optical and thus owns larger operational bandwidths.
