论文标题
矩阵代数之间的映射空间中的凸锥
Convex cones in mapping spaces between matrix algebras
论文作者
论文摘要
我们介绍了基质代数之间的正线性图的单方面映射锥的概念。这些是地图的凸锥，它们在组成下不变，左侧或右侧完全正面地图。可以用放大图来表征此类凸锥的二元组，这也可以用来表征量子信息理论中的许多概念 - 例如，可分离性，纠缠破裂的地图，schmidt数字以及可分解的地图和$ k $ $ $ $ $ - $ $ - $ - 质量图。实际上，这种特征才能达到且仅当涉及的锥体是单方面的映射锥体时。通过此分析，我们获得了锥体组成的映射特性，从中，我们还获得了PPT（阳性部分转置）方形构想的几个等效陈述。
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.
