The question of detecting and quantifying entanglement is central to quantum information theory (QIT). Intimately related to positivity, entanglement detection has been shown to be an NP-hard problem. The state-of-the-art algorithms for deciding whether a quantum state is entangled use SDP (semidefinite programming) hierarchies.

These approaches establish a strong connection between QIT on one side and polynomial optimization, SDP hierarchies, and sum-of-squares (SOS) certificates, on the other. Tools for proving the existence of SOS certificates are of central importance to analyzing the performance of these methods.

Other problems in QIT (de Finetti theorems, symmetric state extensions, absolute separability, positive but not completely positive maps between matrix algebras) admit very natural descriptions in terms of linear matrix inequalities or can be described in terms of polynomial optimization.

The main goal of this workshop is bring together experts in the different mathematical subjects of relevance and mathematicians working on QIT, in order foster the exchange of ideas and problems between the different communities.

**Organization committee**

Ion Nechita (IRSAMC), Mireille Capitaine (IMT), Serban T. Belinschi (IMT)

View online : http://www.math.univ-toulouse.fr/lm…