We consider the important class of quantum operations (completely positive trace-preserving maps) called entanglement breaking channels. We show how every such channel induces stochastic matrix representations that have the same non-zero spectrum as the channel. We then use this to investigate when entanglement breaking channels are primitive, and prove this depends on primitivity of the matrix representations. This in turn leads to tight bounds on the primitivity index of entanglement breaking channels in terms of the primitivity index of the associated stochastic matrices. We also present examples and discuss open problems generated by the work.

中文翻译：

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纠缠破坏通道、随机矩阵和本原性

我们考虑称为纠缠破坏通道的一类重要的量子操作（完全正迹保留映射）。我们展示了每个这样的通道如何诱导具有与通道相同的非零频谱的随机矩阵表示。然后我们使用它来研究何时纠缠破坏通道是原始的，并证明这取决于矩阵表示的原始性。这反过来导致在相关随机矩阵的原始指数方面对纠缠破坏通道的原始指数有严格的限制。我们还提供了示例并讨论了工作产生的开放性问题。