Partially Entanglement Breaking Maps and Right CP-Invariant Cones
There are many results in quantum computing that give ways of characterizing classes of density matrices in terms of other classes of linear maps, and vice-versa – Horodecki’s theorem for positive entanglement witnesses, Terhal and Horodecki’s theorem for density matrices with Schmidt Number at most k, and so on. The goal of this talk is to determine for which sets of linear maps and density matrices these types of relationships hold. Along the way a characterization of Partially Entanglement Breaking maps will be given, and it will be shown that many of their well-known characterizations follow simply because they form a cone that is invariant under right composition with CP maps – a fact that is trivial to check.
- Typed notes [pdf]
- Mapping Cones are Operator Systems – a paper showing that right CP-invariant cones naturally arise from operator systems