Codes and Expansions (CodEx) Seminar

Vern Paulsen (University of Waterloo)
Entanglement Breaking Maps and Zauner's Conjecture

Most approaches to Zauner's conjecture require exact arithmetic. We use completely positive maps to reduce this conjecture to determining the value of an integer valued parameter, that we call the entanglement breaking rank, of a particular completely positive map. We show that this parameter is lower semicontinuous so that is enough to get upper bounds on this rank for maps near the map of interest. We will only assume that the audience is familiar with frame theory and basic facts about positive semidefinite matrices.