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Quantum reverse hypercontractivity: its tensorization and application to strong converses

Presented by: 
Cambyse Rouzé
Friday 27th July 2018 - 11:00 to 11:45
INI Seminar Room 1
Hypercontractivity and log-Sobolev inequalities have found interesting applications in information theory in the past few years. In particular, recently a strong converse bound for the hypothesis testing problem have been proven based on the reverse hypercontractivity inequalities. This talk is about the generalization of this application to the quantum setting. First, the theory of quantum reverse hypercontractivity and its equivalence with the log-Sobolev inequalities will be discussed. To this end, the problem of the tensorization of quantum hypercontractivity inequalities will be addressed. Next, it is shown how quantum reverse hypercontractivity inequalities can be used for proving strong converse bounds in the quantum setting.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons