title: Finite de Finetti theorem for infinite-dimensional systems.
abstract: 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 |Psi/Psi| chosen from a family of subsets {Cn} 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 {Cn}.
authors.affiliation: Department of Mathematics, Royal Holloway, University of London, United Kingdom. C.H.D-Cruz@rhul.ac.uk
authors.forename: Christian
authors.initials: C
authors.lastname: D'Cruz
authors.forename: Tobias J
authors.initials: TJ
authors.lastname: Osborne
authors.forename: Rüdiger
authors.initials: R
authors.lastname: Schack