论文标题
BISCOCHASIC运算符和量子随机变量
Bistochastic operators and quantum random variables
论文作者
论文摘要
给定一个积极的操作员可容纳的度量$ν$作用于局部紧凑的Hausdorff Space $ x $的鲍雷尔集合，并在代数$ \ Mathcal b（\ Mathcal H）中的结果，所有有限的操作员的所有有限的操作员（可能是无限的）$ \ nilbert Space $ \ natercal $ \ Mathcal $ \ - 可以考虑\ MATHCAL B（\ MATHCAL H）$是正量子随机变量。我们对这些功能的跨度定义了一个eminorm，该功能在商中导致了Banach空间。然后，我们考虑在此空间上作用于该空间，然后将量子随机变量的大量化定义，相对于这些操作员。与经典的主要化理论一样，在这种情况下，我们将主要化与涉及某种类型的所有可能凸功能的不平等联系起来。与经典环境不同，整个工作中都会出现连续性和融合问题。
Given a positive operator-valued measure $ν$ acting on the Borel sets of a locally compact Hausdorff space $X$, with outcomes in the algebra $\mathcal B(\mathcal H)$ of all bounded operators on a (possibly infinite-dimensional) Hilbert space $\mathcal H$, one can consider $ν$-integrable functions $X\rightarrow \mathcal B(\mathcal H)$ that are positive quantum random variables. We define a seminorm on the span of such functions which in the quotient leads to a Banach space. We consider bistochastic operators acting on this space and majorization of quantum random variables is then defined with respect to these operators. As in classical majorization theory, we relate majorization in this context to an inequality involving all possible convex functions of a certain type. Unlike the classical setting, continuity and convergence issues arise throughout the work.
