Right mean for the $\alpha-z$ Bures-Wasserstein quantum divergence
Mathematical Physics
2022-01-12 v1 math.MP
Quantum Physics
Abstract
A new quantum divergence induced from the Renyi relative entropy, called the Bures-Wasserstein quantum divergence, has been recently introduced. We investigate in this paper properties of the right mean, which is a unique minimizer of the weighted sum of Bures-Wasserstein quantum divergences to each points. Many interesting operator inequalities of the right mean with the matrix power mean including the Cartan mean are presented. Moreover, we verify the trace inequality with the Wasserstein mean and provide bounds for the Hadamard product of two right means.
Cite
@article{arxiv.2201.03732,
title = {Right mean for the $\alpha-z$ Bures-Wasserstein quantum divergence},
author = {Miran Jeong and Jinmi Hwang and Sejong Kim},
journal= {arXiv preprint arXiv:2201.03732},
year = {2022}
}