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PreprintCC BY 4.0arXiv

Generalized Fidelity, the Data Processing Inequality, and Convexity

  • Haobo Ma
  • Reza Rajaei
  • Wenlin Zhang
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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≥2. 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≥2.

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Cite

BibTeXRIS
BibTeX
@misc{ma2026generalized,
  title = {{Generalized Fidelity, the Data Processing Inequality, and Convexity}},
  author = {Haobo Ma and Reza Rajaei and Wenlin Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.09753},
  eprint = {2609.09753},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09753},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Fidelity, the Data Processing Inequality, and Convexity
AU  - Haobo Ma
AU  - Reza Rajaei
AU  - Wenlin Zhang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.09753
UR  - https://arxiv.org/abs/2609.09753
AB  - 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≥2. 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≥2.
ER  -