  We study the hybrid classical-quantum version of the channel coding problem
for the famous Gel'fand-Pinsker channel. In the classical setting for this
channel the conditional distribution of the channel output given the channel
input is a function of a random parameter called the channel state. We study
this problem when a rate limited version of the channel state is available at
the encoder for the classical-quantum Gel'fand-Pinsker channel. We establish
the capacity region for this problem in the information-spectrum setting. The
capacity region is quantified in terms of spectral-sup classical mutual
information rate and spectral-inf quantum mutual information rate.
