Entanglement and the truncated moment problem

Fabian Bohnet-Waldraff 1, 2 Daniel Braun 2 Olivier Giraud 1

Physical Review A, American Physical Society, 2017, 96 (3), pp.032312. 〈10.1103/PhysRevA.96.032312〉

We map the quantum entanglement problem onto the mathematically well-studied truncated moment problem. This yields a necessary and sufficient condition for separability that can be checked by a hierarchy of semi-definite programs. The algorithm always gives a certificate of entanglement if the state is entangled. If the state is separable, typically a certificate of separability is obtained in a finite number of steps and an explicit decomposition into separable pure states can be extracted.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. Institut für Physikalische und Theoretische Chemie