A Finite de Finetti Theorem for Infinite-Dimensional Systems
  We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state chosen from a family of subsets C_n of the full symmetric subspace for $n$ subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family C_n. 
Christian D'Cruz, Tobias J. Osborne, Ruediger Schack (Royal Holloway,   University of London)