We study a class of qubit non-Markovian general Pauli dynamical maps with multiple singularities in the generator. We discuss a few easy examples involving trigonometric or other nonmonotonic time dependence of the map, and discuss in detail the structure of channels which don’t have any trigonometric functional dependence. We demystify the concept of a singularity here, showing that it corresponds to a point where the dynamics can be regular but the map is momentarily noninvertible, and this gives a basic guideline to construct such non-invertible non-Markovian channels. Most members of the channels in the considered family are quasi-eternally non-Markovian (QENM), which is a broader class of non-Markovian channels than the eternal non-Markovian channels. Specifically, the measure of quasi-eternal non-Markovian (QENM) channels in the considered class is shown to be 23 in the isotropic case, and about 0.96 in the anisotropic case.

中文翻译：

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一类准永恒非马尔可夫泡利通道及其测度

我们研究了一类在生成器中具有多个奇点的量子比特非马尔可夫一般泡利动态映射。我们讨论了一些涉及映射的三角函数或其他非单调时间依赖性的简单示例，并详细讨论了不具有任何三角函数依赖性的通道结构。我们在这里揭开奇点的概念，表明它对应于动态可以是规则的但映射暂时不可逆的点，这为构建这种不可逆的非马尔可夫通道提供了基本指导。所考虑的家族中的大多数通道成员都是准永恒非马尔可夫（QENM），这是比永恒非马尔可夫通道更广泛的非马尔可夫通道类别。具体来说，23在各向同性情况下，在各向异性情况下约为 0.96。