The \(\alpha\)-\(z\)-Bures Wasserstein divergence

DOI10.1016/j.laa.2021.04.007OpenAlexW3159818672MaRDI QIDQ2029836

Trung Dung Vuong, Dinh Trung Hoa, Bich-Khue T. Vo, Lê Công-Trình

Publication date: 4 June 2021

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2021.04.007

zbMATH Keywords

least squares problemKarcher meanquantum divergencedata processing inequalitymatrix power meanin-betweenness property\(\alpha\)-\(z\) Bures distance

Mathematics Subject Classification ID

Linear operator inequalities (47A63) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56)

Related Items (8)

The matrix Heinz mean and related divergence ⋮ On a parametric family of distance measures that includes the Hellinger and the Bures distances ⋮ \(\alpha\)-\(z\)-Rényi relative entropy related quantities and their preservers ⋮ Right mean for the \(\alpha - z\) Bures-Wasserstein quantum divergence ⋮ Weak log-majorization and inequalities of power means ⋮ Unnamed Item ⋮ Some matrix equations involving the weighted geometric mean ⋮ Geodesic in-betweenness for means of several matrices

Cites Work

• Unnamed Item
• Matrix power means and the Karcher mean
• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Rényi relative entropy
• Some geometric properties of matrix means with respect to different metrics
• Some operator and trace function convexity theorems
• In-betweenness, a geometrical monotonicity property for operator means
• The Rényi power means of matrices
• Quantum divergences with \(p\)-power means
• Matrix versions of the Hellinger distance
• On the Bures-Wasserstein distance between positive definite matrices
• Generalized Hellinger metric and Audenaert's in-betweenness
• On the monotonicity of weighted power means for matrices
• Strong convexity of sandwiched entropies and related optimization problems
• Weighted Hellinger distance and in-betweenness property
• α-z-Rényi relative entropies
• A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite Matrices
• In-sphere property and reverse inequalities for matrix means

This page was built for publication: The \(\alpha\)-\(z\)-Bures Wasserstein divergence