We study the memory property of the channels obtained by convex combinations of Markovian channels that are not necessarily quantum dynamical semigroups (QDSs). In particular, we characterize the geometry of the region of (non-)Markovian channels obtained by the convex combination of the three Pauli channels, as a function of deviation from the semigroup form in a family of channels. The regions are highly convex, and interestingly, the measure of the non-Markovian region shrinks with greater deviation from the QDS structure for the considered family, underscoring the counterintuitive nature of (non-)Markovianity under channel mixing.

中文翻译：

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非半群的 CP 可分泡利通道的凸组合

我们研究了通过马尔可夫通道的凸组合获得的通道的记忆特性，这些通道不一定是量子动力学半群 (QDS)。特别地，我们将通过三个泡利通道的凸组合获得的（非）马尔可夫通道区域的几何特征表征为与通道族中半群形式的偏差的函数。这些区域是高度凸的，有趣的是，非马尔可夫区域的度量随着与所考虑家族的 QDS 结构的更大偏差而缩小，强调了通道混合下（非）马尔可夫性的违反直觉的性质。