Aljaž Zalar: There are many more positive maps than completely positive maps
Source: Algebra and functional analysis seminar
Abstract: A linear map between real symmetric matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. We will present quantitative bounds on the fraction of positive maps that are completely positive. Main tools are the real algebraic geometry techniques developed by Blekherman to study the gap between positive polynomials and sums of squares. If time allows, an algorithm to produce positive maps which are not completely positive will be presented. This is joint work with Igor Klep, Scott McCullough and Klemen Šivic.
Roman Drnovšek in Primož Moravec