Year: 2026
Type: preprint
Abstract: In this paper, we show that the generalized Bures--Wasserstein distance induced by the generalized fidelity fails the data processing inequality (DPI) in every dimension $n\geq2$. In dimension two, we derive three sufficient conditions guaranteeing the DPI 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. We also show that neither the generalized Bures--Wasserstein distance nor its square is convex in one state, even with the other state and the reference fixed, in every dimension $n\geq2$.
Source: arXiv (Cornell University)
Authors: Ma, Haobo, Rajaei, Reza, Zhang, Wenlin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212136440