---
res:
bibo_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.
@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Jozsef
foaf_name: Pitrik, Jozsef
foaf_surname: Pitrik
- foaf_Person:
foaf_givenName: Daniel
foaf_name: Virosztek, Daniel
foaf_surname: Virosztek
foaf_workInfoHomepage: http://www.librecat.org/personId=48DB45DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0003-1109-5511
bibo_doi: 10.1007/s11005-020-01282-0
bibo_issue: '8'
bibo_volume: 110
dct_date: 2020^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0377-9017
- http://id.crossref.org/issn/1573-0530
dct_language: eng
dct_publisher: Springer Nature@
dct_title: Quantum Hellinger distances revisited@
...