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Linear Analysis Seminar

Date: December 1, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Li Gao, University of Illinois at Urbana-Champaign


Title: Entropic uncertainty relations via Noncommutative Lp Spaces

Abstract: The Heisenberg uncertainty principle states that it is impossible to prepare a quantum particle for which both position and momentum are sharply defined. Entropy is a natural measure of uncertainty. The first entropic formulation of the uncertainty principle was proved by Hirschman and since then entropic uncertainty relations have been obtained for many different scenarios, including some recent advances on uncertainty relations with quantum memory. In this talk, I will present an approach to entropic uncertainty relations via noncommutative Lp norms. We show that the natural connection between noncommutative Lp Spaces and Renyi information measure gives certain uncertainty relation for two complementary subalgebras of a tracial von Neumann algebra. This is a joint work with Marius Junge and Nicholas LaRacuente.