由小集合生成映射锥
Generation of Mapping Cones from Small Sets
摘要：
我们对最近提出的一个问题做出了肯定的回答，该问题询问是否存在“非典型”凸映射锥--即，一个不是从转置映射和锥的k-正和k-超映射。我们明确地构造这样一个锥的基础上原子的积极地图。我们的一般技巧是考虑由单个映射生成的最小凸映射锥，并得到了关于这类映射锥的几个结果。我们使用这种技术，也提出了其他几个例子，非典型的映射锥，包括家庭的自旋因子产生的锥。我们还提供了一个完整的表征映射锥产生的单元素在量子比特的情况下，在其典型性。
英文摘要：
We answer in the affirmative a recently-posed question that asked if there exists an "untypical" convex mapping cone -- i.e., one that does not arise from the transpose map and the cones of k-positive and k-superpositive maps. We explicitly construct such a cone based on atomic positive maps. Our general technique is to consider the smallest convex mapping cone generated by a single map, and we derive several results on such mapping cones. We use this technique to also present several other examples of untypical mapping cones, including a family of cones generated by spin factors. We also provide a full characterization of mapping cones generated by single elements in the qubit case in terms of their typicality.
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