Abstract
This talk begins with the problem whether entanglement exists in all non-classical operational theories. This problem was already considered as a mathematical problem by George Barker in the 70′ in the context of ordered vector spaces; here we discuss some aspects of the proof that entanglement is a generic feature of non-classical theories. As a consequence of this result, the need for mathematical tools to detect entanglement in all operational theories arises, we address this issue by presenting a generalization of the Doherty-Parrilo-Spedalieri (DPS) hierarchy to operational theories and we also mention the cases when such hierarchy is finite. Finally we discuss the unexpected applications of these results to solve current problems in quantum information, we mainly focus on the problem of semi-device independent certification of Schmidt number of quantum states, for which we derive tight SDP hierarchy.
