Generalized Fidelity, the Data Processing Inequality, and Convexity

2026-10-22 · arXiv Quantum Physics

arXiv:2609.09753v3 Announce Type: replace

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 $n\geq2$.

原文链接：https://arxiv.org/abs/2609.09753

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