论文标题
由点，广义仿射约束和量子理论产生的面孔
The face generated by a point, generalized affine constraints, and quantum theory
论文作者
论文摘要
我们分析了由任意凸集中点及其相对代数内部的点产生的面孔，这是我们应证明的非空置。我们表明，通过将凸集与广义仿射功能的级别或水平集相交，点由点产生的面尺寸最多可能会减小。我们将结果应用于可分离的希尔伯特空间上的一组量子状态。除其他外，我们表明，每个国家都有任何两个（不一定是有限的）积极操作员的预期值有限的预期值，将其分解为具有相同预期值的纯状态。我们讨论量子信息理论中的应用。
We analyze faces generated by points in an arbitrary convex set and their relative algebraic interiors, which are nonempty as we shall prove. We show that by intersecting a convex set with a sublevel or level set of a generalized affine functional, the dimension of the face generated by a point may decrease by at most one. We apply the results to the set of quantum states on a separable Hilbert space. Among others, we show that every state having finite expected values of any two (not necessarily bounded) positive operators admits a decomposition into pure states with the same expected values. We discuss applications in quantum information theory.
