Quantum Hellinger distances revisited

@article{Pitrik2019QuantumHD,
  title={Quantum Hellinger distances revisited},
  author={J. Pitrik and D'aniel Virosztek},
  journal={Letters in Mathematical Physics},
  year={2019},
  pages={1-14}
}
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 $$\phi (A,B)=\mathrm {Tr} \left( (1-c)A + c B - A \sigma B \right) ,$$ ϕ ( A , B ) = Tr ( 1 - c ) A + c B - A σ B , where $$\sigma $$ σ is an arbitrary Kubo–Ando mean, and $$c \in (0,1)$$ c ∈ ( 0 , 1 ) is the weight of $$\sigma… Expand
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Correction to: Matrix versions of the Hellinger distance
Theorem 9 in our paper [1] is wrong. The statement should be replaced by the following.

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