Riemannian-geometric generalizations of quantum fidelities and Bures-Wasserstein distance
Year: 2025
Type: article
Abstract: We introduce a family of fidelities, termed generalized fidelity, which are based on the Riemannian geometry of the Bures-Wasserstein manifold. We show that this family of fidelities generalizes standard quantum fidelities such as Uhlmann-, Holevo-, and Matsumoto-fidelity and demonstrate that it satisfies analogous celebrated properties. The generalized fidelity naturally arises from a generalized Bures distance, the natural distance obtained by linearizing the Bures-Wasserstein manifold. We prove various invariance and covariance properties of generalized fidelity as the point of linearization moves along geodesic-related paths. We also provide a Block-matrix characterization and prove an Uhlmann-like theorem, as well as provide further extensions to the multivariate setting and to quantum Rényi divergences, generalizing Petz-, Sandwiched-, Reverse sandwiched-, and Geometric-Rényi divergences of order α.
Source: Journal of Mathematical Physics
DOI: 10.1063/5.0252803
Authors: A. Afham, Chris Ferrie
Institution: University of Technology Sydney
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4413012818