On Equality of Complete Positivity and Complete Copositivity of Positive Map

Abstract

In this paper we construct a 2-positive map from M4(C) to M5(C) and state the conditions under which the map is positive and completely positive (copositivity of positive). The construction allows us to create a decomposable map, where the Choi matrix of complete positivity is equal to the Choi matrix of complete copositivity.