Entanglement and the truncated moment problem

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 semidefinite 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.

Figure 1

Flow diagram to visualize the algorithm. “Solve SDP” refers to Eqs. (29, 30, 31, 32).