论文标题
$ c^*$ - 纠缠破坏地图的极端点
$C^*$-extreme points of entanglement breaking maps
论文作者
论文摘要
在本文中，我们研究了矩阵代数上的$ c^*$ - 凸出的纠缠破裂（EB-）地图。讨论了$ c^*$ - 极端点的一般属性和抽象表征。通过为一类EB-MAPS建立radon-nikodym类型定理，我们对$ c^*$ - 极端点进行了完整的描述。结果表明，一个Unital EB-MAP $φ：m_ {d_1} \ to m_ {d_2} $是$ c^*$ - 极限 - 仅当它的cho-rank等于$ d_2 $时。最后，作为EB-MAPS孔形式的直接结果，我们得出了Krein-Milman定理的非共同类似物，以$ C^*$ - 一组Unital Eb-Maps的凸度。
In this paper we study the $C^*$-convex set of unital entanglement breaking (EB-)maps on matrix algebras. General properties and an abstract characterization of $C^*$-extreme points are discussed. By establishing a Radon-Nikodym type theorem for a class of EB-maps we give a complete description of the $C^*$-extreme points. It is shown that a unital EB-map $Φ:M_{d_1}\to M_{d_2}$ is $C^*$-extreme if and only if it has Choi-rank equal to $d_2$. Finally, as a direct consequence of the Holevo form of EB-maps, we derive a noncommutative analogue of the Krein-Milman theorem for $C^*$-convexity of the set of unital EB-maps.
