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University of Cambridge > Talks.cam > Isaac Newton Institute Seminar Series > Renyi relative entropies and noncommutative L_p-spaces

## Renyi relative entropies and noncommutative L_p-spacesAdd to your list(s) Download to your calendar using vCal - Anna Jenčová (Slovak Academy of Sciences)
- Thursday 26 July 2018, 16:00-16:45
- 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 The standard quantum Renyi relative entropies belong to the class of Petz quantum f-divergences and have a number of applications in quantum information theory, including and operational interpretation as error exponents in quantum hypothesis testing. In the last couple of years, the sandwiched version of Renyi relative entropies gained attention for their applications in various strong converse results. While the Petz f-divergences are defined for arbitrary von Neumann algebras, the sandwiched version was introduced for density matrices. In this contribution, it is shown that these quantities can be extended to infinite dimensions. To this end, we use the interpolating family of non-commutative L_p-spaces with respect to a state, defined by Kosaki. This definition provides us with tools for proving a number of properties of the sandwiched Renyi entropies, in particular the data processing inequality with respect to normal unital (completely) positive maps. It is also shown that this definition coincides with the previously introduced Araki-Masuda divergences by Berta et. al. 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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