纠缠破缺映射的$C^*$ -极值点
$C^*$-extreme points of entanglement breaking maps
摘要：
本文研究矩阵代数上单位纠缠破缺（EB-）映射的$C^*$ -凸集.讨论了$C^*$ -极值点的一般性质和抽象刻画。通过建立一类EB-映射的Radon-Nikodym型定理，给出了$C^*$ -极值点的完整刻画.证明了单位EB映射$Φ:M_{d_1}\to M_{d_2}$是$C^*$ -极值的充要条件是它的Choi秩等于$d_2$ .最后，作为EB-映射的Holevo形式的直接结果，我们导出了单位EB-映射集的$C^*$ -凸性的Krein-Milman定理的一个非交换类似定理。
英文摘要：
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.
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