Entanglement and the truncated moment problem

Understand

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.