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We study subadditivity of the minimum output entropy ($H_{min}$) of quantummultiple access channels (MACs). We provide an example of violation of theadditivity theorem for $H_{min}$ known in classical information theory. Ourresult is based on a fundamental property of $MACs$ i.e. independence of eachsender. The channels used in the example can be constructed explicitly. On thebasis of subadditivity of $H_{min}$ we also provide an example of extremalsuperadditivity (super activation) of the classical capacity region of MACs.

Subadditivity of the minimum output entropy and superactivation of the classical capacity of quantum multiple access channels