Free Probability and Operators

Date: May 12, 2023

Time: 4:00PM - 5:00PM

Location: BLOC 306, ZOOM

Speaker: Jurij Volcic, Drexel University

Title: State polynomials: positivity and applications

Abstract: State polynomials are polynomial expressions in operator variables and formal states of their products. This talk addresses state polynomials whose evaluations on states and tuples of operators on a Hilbert space are positive. The most well-known occurrence of such a positive state polynomial in disguise is the Cauchy-Schwarz inequality. Much more recently, positive state polynomials emerged as nonlinear Bell inequalities for quantum networks. The talk presents the state polynomial analog of Hilbert's 17th problem, and an algebraic certificate for constrained positivity. The latter is used to design a scheme for state polynomial optimization, which resolves a few questions from quantum information theory.

ZOOM LINK: https://tamu.zoom.us/j/97716603515