  In this paper we are interested to model quantum signal by statistical signal
processing methods. The Gaussian distribution has been considered for the input
quantum signal as Gaussian state have been proven to a type of important robust
state and most of the important experiments of quantum information are done
with Gaussian light. Along with that a joint noise model has been invoked, and
followed by a received signal model has been formulated by using convolution of
transmitted signal and joint quantum noise to realized theoretical achievable
capacity of the single quantum link. In joint quantum noise model we consider
the quantum Poisson noise with classical Gaussian noise. We compare the
capacity of the quantum channel with respect to SNR to detect its overall
tendency. In this paper we use the channel equation in terms of random variable
to investigate the quantum signals and noise model statistically. These methods
are proposed to develop Quantum statistical signal processing and the idea
comes from the statistical signal processing.
