A complete hierarchy for the pure state marginal problem in quantum mechanics

Clarifying the relation between whole and its parts is crucial for many problems in science. In quantum mechanics, this question manifests itself marginal problem, which asks whether there a global pure state some given marginals. This problem arises contexts, ranging from chemistry to entanglement theory error correcting codes. paper, we prove correspondence of separability problem. Based on this, describe sequence semidefinite programs can decide marginals are compatible with state. As an application, that existence multiparticle absolutely maximally entangled states dimension equivalent explicitly two-party Finally, show codes parameters also be interpreted as hence, our complete hierarchy used.