发表机构
University of Oklahoma（俄克拉荷马大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究广义保真度诱导的Bures-Wasserstein距离是否满足数据处理不等式，发现高维不满足，二维给出充分条件，并给出退化为Uhlmann保真度的充要条件。
AI 中文摘要
在本文中，我们证明了由广义保真度诱导的广义Bures--Wasserstein距离在维数大于2时不满足数据处理不等式。在二维情形下，尽管我们未能完全解决一般情况下的DPI，但通过使用广义保真度实部的显式公式，我们推导出两个保证其成立的充分条件。此外，我们找到了广义保真度退化为Uhlmann保真度的充要条件。
英文摘要
In this note, we show that the generalized Bures--Wasserstein distance induced by the generalized fidelity does not satisfy the data processing inequality in dimensions greater than two. In dimension two, although we do not settle the DPI in full generality, we derive two sufficient conditions guaranteeing it by using an explicit formula for the real part of the generalized fidelity. Furthermore, we find a necessary and sufficient condition under which the generalized fidelity reduces to the Uhlmann fidelity. Lastly, we will show that the generalized Bures--Wasserstein distance is not convex in dimensions greater than two.
