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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Quantum f-divergences in von Neumann algebras - Fu
mio Hiai (Tohoku University )
DTSTART;TZID=Europe/London:20180726T144500
DTEND;TZID=Europe/London:20180726T153000
UID:TALK108397AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/108397
DESCRIPTION:This talk is a comprehensive survey on recent deve
lopments of quantum divergences in general von Neu
mann algebras\, including standard f-divergences\,
maximal f-divergences\, and R\\'\;enyi type di
vergences\, whose mathematical backgrounds are Haa
gerup'\;s L^p-spaces and Araki'\;s relative
modular operator. Standard f-divergences were form
erly studied by Petz in a bit more general form wi
th name quasi-entropy\, whose most familiar one is
the relative entropy initiated by Umegaki and ext
ended to general von Neumann algebras by Araki. We
extend Kosaki'\;s variational expression of th
e relative entropy to an arbitrary standard f-dive
rgence\, from which most important properties of s
tandard f-divergences follow immediately. We also
go into standard R\\'\;enyi divergences (as a v
ariation of standard f-divergences) in some detail
\, and touch briefly sandwiched R\\'\;enyi dive
rgences in von Neumann algebras\, which have recen
tly been developed by Jen\\v cov\\'\;a and Bert
a-Scholz-Tomamichel. Finally\, we treat maximal f-
divergences and discuss their definition\, integra
l expression\, and comparison with standard f-dive
rgences. This talk is dedicated to the memory of D
\\'\;enes Petz.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:INI IT
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