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DTSTART:20190331T030000
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DTSTART:20191027T020000
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DTSTAMP:20200125T180937Z
UID:5b4d8fb087015241973140@ist.ac.at
DTSTART:20190523T160000
DTEND:20190523T180000
DESCRIPTION:Speaker: Daniel Virosztek\nAbstract: Barycenters (or mean squar
ed error estimators) play a distinguished role in statistics and informati
on theory. This concept is boring in Euclidean spaces in the sense that it
coincides with the weighted average. However\, non-Euclidean metrics and
other distance-like functions (such as relative entropies) are often more
natural than the flat metric from the viewpoint of applications.First\, we
take the submanifold of centered Gaussian measures in the space of square
integrable random variables in R^d endowed with the optimal transport (Wa
sserstein) distance to illustrate the challenges of computing the barycent
er in non-flat metrics. We will also discuss the closely related Riemannia
n trace metric on positive operators\, which is defined by the Hessian of
the Boltzmann entropy\, from this viewpoint.Then we turn to quantum inform
ation theory and consider generalized quantum Hellinger divergences\, that
belong to the family of maximal quantum f-divergences and behave like squ
ared distances in some sense to be clarified during the talk.We derive a c
haracterization of the barycenters for these divergences and compare our r
esults to those of Bhatia et al. [Lett. Math. Phys. (2019)\, in press (htt
ps://doi.org/10.1007/s11005-019-01156-0)\, arXiv:1901.01378v1 (https://arx
iv.org/abs/1901.01378)]. We note that the characterization given by Bhatia
et al. is not correct in general\, albeit it is true for commuting operat
ors.Based on joint work with Jozsef Pitrik (arXiv:1903.10455 (https://arxi
v.org/abs/1903.10455))
LOCATION:Big Seminar room Ground floor / Office Bldg West (I21.EG.101)\, IS
T Austria
ORGANIZER:cpetz@ist.ac.at
SUMMARY:Barycenters in quantum information theory
URL:https://talks-calendar.app.ist.ac.at/events/1884
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