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Since the discovery of quantum entanglement, characterization and detection of multipartite entanglement has remained an open question. In this work, we present how one can map the separability problem onto the truncated moment problem in probability theory. It leads to a necessary and sufficient condition for the separability of arbitrary quantum systems with arbitrary symmetries between the subparts. A semidefinite algorithm is presented, whose outcome provides a certificate of separability, or entanglement.

Entanglement --- Semidefinite optimization --- Truncated moment problem --- Convex optimization --- Separability problem --- Certificate of entanglement --- Certificate of separability --- Intrication --- Optimisation semidefinite --- Problème des moments tronqué --- Optimisation convexe --- Problème de la séparabilité --- Certificat d'intrication --- Certificat de séparabilité --- Physique, chimie, mathématiques & sciences de la terre > Physique