# Aljaž Zalar: There are many more positive maps than completely positive maps

Date: 9. 1. 2017

Source: Algebra and functional analysis seminar

Source: Algebra and functional analysis seminar

Četrtek, 12. 1. 2017, ob 12:30 v predavalnici 2.03, FMF, Jadranska 21, Ljubljana

**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.

Vljudno vabljeni!

Roman Drnovšek in Primož Moravec