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arXiv · 1209.0437

Generation of Mapping Cones from Small Sets

Nathaniel Johnston·Łukasz Skowronek·Erling Størmer
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Abstract

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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Nathaniel Johnston, Łukasz Skowronek, Erling Størmer. 2012-09-03. Generation of Mapping Cones from Small Sets. https://doi.org/10.1016/j.laa.2012.12.007

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