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.

中文翻译：

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通过对半圆形和圆形元素的强收敛来破坏量子通道的可加性

在大多数情况下，对于由 Haar 分布酉矩阵定义的随机量子信道，证明了在量子通信中显示非经典特性的最小输出熵的可加性违反。在本文中，我们研究了由 Gaussian Unitary Ensembles 和 Ginibre Ensembles 组成的随机完全正映射。使用半圆系统和自由概率循环系统，我们不仅证明了在渐近状态下最大输出范数的乘法违反，而且还通过 Haagerup 不等式证明了通过完全纠正上述构造的一类新的随机量子通道的可加性违反基于强收敛的正映射。