Abstract: Many problems in quantum informationtheory are connected to properties of positive linear maps betweenmatrix algebras. After a brief introduction to some basic concepts ofquantum information theory I want to focus on the problem ofentanglement distillation. I will explain how this problem isconnected to the existence problem of positive linear maps that staypositive under taking tensor powers and that are neither completelypositive nor completely co-positive. If time permits I will outlinesome constructions of interesting positive maps and hownon-decomposability arises naturally from tensorisation.
