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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Quantum f-divergences in von Neumann algebras

## Quantum f-divergences in von Neumann algebrasAdd to your list(s) Download to your calendar using vCal - Fumio Hiai (Tohoku University )
- Thursday 26 July 2018, 14:45-15:30
- Seminar Room 1, Newton Institute.
If you have a question about this talk, please contact INI IT. MQIW05 - Beyond I.I.D. in information theory This talk is a comprehensive survey on recent developments of quantum divergences in general von Neumann algebras, including standard f-divergences, maximal f-divergences, and R\'enyi type divergences, whose mathematical backgrounds are Haagerup's L^p-spaces and Araki's relative modular operator. Standard f-divergences were formerly studied by Petz in a bit more general form with name quasi-entropy, whose most familiar one is the relative entropy initiated by Umegaki and extended to general von Neumann algebras by Araki. We extend Kosaki's variational expression of the relative entropy to an arbitrary standard f-divergence, from which most important properties of standard f-divergences follow immediately. We also go into standard R\'enyi divergences (as a variation of standard f-divergences) in some detail, and touch briefly sandwiched R\'enyi divergences in von Neumann algebras, which have recently been developed by Jen\v cov\'a and Berta-Scholz-Tomamichel. Finally, we treat maximal f-divergences and discuss their definition, integral expression, and comparison with standard f-divergences. This talk is dedicated to the memory of D\'enes Petz. This talk is part of the Isaac Newton Institute Seminar Series series. ## This talk is included in these lists:- All CMS events
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