@article{7618,
abstract = {This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. },
author = {Pitrik, Jozsef and Virosztek, Daniel},
issn = {1573-0530},
journal = {Letters in Mathematical Physics},
number = {8},
pages = {2039--2052},
publisher = {Springer Nature},
title = {{Quantum Hellinger distances revisited}},
doi = {10.1007/s11005-020-01282-0},
volume = {110},
year = {2020},
}