论文标题
$ c^*$ - 正面运营商的极端要点有价值的措施和一个完全正面地图
$C^*$-extreme points of positive operator valued measures and unital completely positive maps
论文作者
论文摘要
我们研究了可测量的空间上归一化正运算符估价措施（POVM）的量子（$ c^*$）。特别是，可以看出，与经典凸度下的极端点不同，$ c^*$ - 可计数空间（尤其是有限集合）上归一化POVM的极端点始终是光谱措施（归一化投影有价值的措施）。更一般地表明，原子$ c^*$ - 极端点是光谱。还证明了Krein-Milman型定理。作为一个应用程序，显示出具有可计数频谱的任何交换Unital $ c^*$ - 代数（尤其是$ {\ Mathbb c}^n $）的地图是$ c^*$ - 仅当Unital $*$ - $*$ - 同种异体中，仅在一组UNITAL APTRINE MAPS中的$ C^*$。
We study the quantum ($C^*$) convexity structure of normalized positive operator valued measures (POVMs) on measurable spaces. In particular, it is seen that unlike extreme points under classical convexity, $C^*$-extreme points of normalized POVMs on countable spaces (in particular for finite sets) are always spectral measures (normalized projection valued measures). More generally it is shown that atomic $C^*$-extreme points are spectral. A Krein-Milman type theorem for POVMs has also been proved. As an application it is shown that a map on any commutative unital $C^*$-algebra with countable spectrum (in particular ${\mathbb C}^n$) is $C^*$-extreme in the set of unital completely positive maps if and only if it is a unital $*$-homomorphism.
