Senior Honors Thesis Presentation: Measure concentration in complex projective space and quantum entanglement
Speaker: Zheyuan Wu, Washington University in St. Louis
Abstract: We explain, after Patrick Hayden, how concentration inequalities can be used in quantum theory to show that random quantum states associated to high-dimensional bipartite systems are highly entangled with high probability. A geometric interpretation of the concentration phenomenon can be given in terms of Michael Gromov's notion of the observable diameter of families of measure-metric (MM) spaces. We use Hayden's result to obtain estimates for the observable diameter of complex projective spaces.
Faculty Advisor: Renato Feres