Michael Wolf: The Ruskai-Audenaert conjecture and balanced decompositions of positive operators

Speaker
Michael Wolf, Technical University of Munich

Abstract
Several open problems in quantum information theory ask whether a given positive operator admits a ‘balanced’ decomposition — that is, whether it can be written as a sum of positive operators of constrained rank, each uniformly satisfying some (semi)algebraic condition. The SIC-POVM and MUB existence problems are of this type, as is the Ruskai–Audenaert conjecture. In this talk, I will first show how certain problems of this form are amenable to techniques from equivariant cohomology, and then present partial results on the Ruskai–Audenaert conjecture, which concerns the existence of highly symmetric and efficient convex decompositions of quantum channels.