点生成的面、广义仿射约束和量子理论
The face generated by a point, generalized affine constraints, and quantum theory
摘要：
我们分析了在任意凸集和它们的相对代数内部，这是非空的，因为我们将证明点所产生的面。我们证明了，通过相交的凸集的子级或水平集的广义仿射泛函，由一个点生成的面的维数可能减少最多一个。我们将结果应用于可分希尔伯特空间上的量子态集。除其他外，我们表明，每一个国家有有限的期望值的任何两个（不一定有界）正运营商承认分解成纯态具有相同的期望值。我们讨论了在量子信息论中的应用。
英文摘要：
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.
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