论文标题
饱和数据处理不等式的几何条件
Geometric conditions for saturating the data processing inequality
论文作者
论文摘要
数据处理不平等（DPI）是通过对密度矩阵的区分措施满足的标量不平等。对于某些可区分性措施，标量DPI的饱和意味着与该度量参数有关的操作员方程。这些结果通常是使用功能分析技术得出的。在互补方法中，我们使用几何技术来得出一个公式，该公式从DPI饱和度中提供了任何可区分性措施。此外，对于一系列可区分性措施，派生的操作员方程也足以暗示饱和。我们的操作员方程与夹层rényi相对熵的已知结果相吻合，并为$α$ - $ z $ z $rényi相对熵和量子$ f $ divergences的家族提供了新的结果，我们明确地计算出来。
The data processing inequality (DPI) is a scalar inequality satisfied by distinguishability measures on density matrices. For some distinguishability measures, saturation of the scalar DPI implies an operator equation relating the arguments of the measure. These results are typically derived using functional analytic techniques. In a complementary approach, we use geometric techniques to derive a formula that gives an operator equation from DPI saturation for any distinguishability measure; moreover, for a broad class of distinguishability measures, the derived operator equation is sufficient to imply saturation as well. Our operator equation coincides with known results for the sandwiched Rényi relative entropies, and gives new results for $α$-$z$ Rényi relative entropies and a family of of quantum $f$-divergences, which we compute explicitly.
