  Additivity violation of minimum output entropy, which shows non-classical
properties in quantum communication, had been proved in most cases for random
quantum channels defined by Haar-distributed unitary matrices. In this paper,
we investigate random completely positive maps made of Gaussian Unitary
Ensembles and Ginibre Ensembles regarding this matter. Using semi-circular
systems and circular systems of free probability, we not only show the
multiplicativity violation of maximum output norms in the asymptotic regimes
but also prove the additivity violation via Haagerup inequality for a new class
of random quantum channels constructed by rectifying the above completely
positive maps based on strong convergence.
