Convex cones in mapping spaces between matrix algebras
| Autor: | Girard, Mark, Kye, Seung-Hyeok, Størmer, Erling |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Linear Algebra Appl. 608 (2021), 248-269 |
| Druh dokumentu: | Working Paper |
| Popis: | We introduce the notion of one-sided mapping cones of positive linear maps between matrix algebras. These are convex cones of maps that are invariant under compositions by completely positive maps from either the left or right side. The duals of such convex cones can be characterized in terms of ampliation maps, which can also be used to characterize many notions from quantum information theory---such as separability, entanglement-breaking maps, Schmidt numbers, as well as decomposable maps and $k$-positive maps in functional analysis. In fact, such characterizations hold if and only if the involved cone is a one-sided mapping cone. Through this analysis, we obtain mapping properties for compositions of cones from which we also obtain several equivalent statements of the PPT (positive partial transpose) square conjecture. Comment: An earlier version of this paper due to second and third authors originally appeared as arXiv:2002.09614v1. After the first author joined as a co-author, the authors changed the title, rewrote and extended the results of the earlier version |
| Databáze: | arXiv |
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