Entropic bounds for the quantum marginal problem
  The quantum marginal problem asks, given a set of reduced quantum states of a multipartite system, whether there exists a joint quantum state consistent with these reduced states. The quantum marginal problem is known to be hard to solve in general as it is a variant of the N-representability problem. We provide entropic bounds on the number of orthogonal solutions to the quantum marginal problem. 
Tobias J. Osborne