Distinguished Lecture: Stanisław J. Szarek, Case Western Reserve University

Discusses random quantum states and entanglement

All dates for this event occur in the past.

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Distinguished Lecture Title: Random quantum states and entanglement

Speaker: Prof. Stanisław J. Szarek, Case Western Reserve University 

Date: Oct 29, Tuesday 

Time: 1:15pm — 2:15pm

Location: Dreese Lab 260

Abstract: Entanglement is a crucial resource in most schemes aiming at exploiting quantum phenomena to process information, and its understanding and control are indispensable for mastering quantum technologies. In this talk we will describe, in a precise quantitative way, the emergence of entanglement in typical quantum systems. We will start by sketching the mathematical framework needed to state results and then outline the mathematical ideas allowing to show the following "20% Rule": Consider a quantum system consisting of N identical particles  and assume that it is in a random pure state. Let A  and B be two subsystems consisting of k particles each. Then there exists a threshold value K approximately equal to N/5 such that  
- If k > K, then A and B typically share entanglement. 
- If k < K, then A and B typically do not share entanglement.

Bio: Stanisław J. Szarek is a Professor of Mathematics at both Case Western Reserve University and Pierre and Marie Curie University. His primary field is Functional Analysis, more specifically Geometry of Banach Spaces, Convexity. He is also interested in combinatorial and probabilistic aspects of Mathematical Physics, Computer Science, Operator Theory, Approximation Theory, and Operation Research, particularly on Random Matrices and Quantum Information Theory. He earned a master's degree from the University of Warsaw in 1976, and a Ph.D. from the Polish Academy of Sciences in 1979. He continued at the Polish Academy as a research fellow for four years before taking a faculty position at Case, where he is now the Kerr Professor of Mathematics. Prof. Szarek won a gold medal in the 1971 International Mathematical Olympiad. He was an invited speaker at the 2006 International Congress of Mathematicians. In 2007 he won the Langevin Prize of the French Academy of Sciences. In 2012 he became one of the inaugural fellows of the American Mathematical Society and in 2017 he was awarded the Sierpiński medal.