  The quantum marginal problem is concerned with characterizing which
collections of quantum states on different subsystems are compatible in the
sense that they are the marginals of some multipartite quantum state. Presented
here is a countable family of inequalities, each of which is necessarily
satisfied by any compatible collection of quantum states. Additionally, this
family of inequalities is shown to be sufficient: every incompatible collection
of quantum states will violate at least one inequality belonging to the family.
