论文标题
一组古典或量子通道中的可访问地图
Accessible maps in a group of classical or quantum channels
论文作者
论文摘要
我们研究了一组接受组结构的经典和量子通道中可访问性的问题。一组通道的组属性以及分析组$ g $的封闭结构在这方面起关键作用。组元素的所有凸组合的集合包含一个可以通过动力学半集团访问的通道子集。我们证明，可访问的通道是由组元素的凸组合的概率向量确定的，这既不取决于通道ACT的空间的维度，也不取决于组的特定表示。研究集合的$ \ Mathcal {a} $的几何特性，我们表明该集合是非convex，但相对于该组的所有元素的均匀混合物，它都享有星形属性。我们证明了集合$ \ MATHCAL {a} $涵盖了组元素的所有凸组合的正面。
We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group $G$ plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible channels are determined by probability vectors of weights of a convex combination of the group elements, which depend neither on the dimension of the space on which the channels act, nor on the specific representation of the group. Investigating geometric properties of the set $\mathcal{A}$ of accessible maps we show that this set is non-convex, but it enjoys the star-shape property with respect to the uniform mixture of all elements of the group. We demonstrate that the set $\mathcal{A}$ covers a positive volume in the polytope of all convex combinations of the elements of the group.
