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Free compression norms and Lp norms

Wednesday 4th September 2013 - 15:30 to 16:30
INI Seminar Room 1
Co-authors: Serban Belinschi (Queen's), Ion Nechita (CNRS, Toulouse UPS)

I will talk about a new norm that shows up naturally in the framework of random quantum channels. This norm relies on free probability theory and is called the free compression norm. We show that the problem of comparing it to Lp norms has applications to the understanding of the minimum output entropy (MOE) of typical quantum random channels. As an application, we establish violation of additivity of the MOE for typical quantum channels with Bell states, and find in this framework the optimal output dimension and the optimal violation.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons